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JEE (Main+Advanced), , Circle, , Exercise – I (Level - 01), , 8., , (a) x 2  y 2  5 x  0, , Section (A) : Equation of circle, Intercepts on axes, 1., The length of the diameter of the circle, , (b) 2 x 2  2 y 2  5 x  0, , x  y  4 x  6 y  4  0 is 2, , 2., , 2, , (a) 9, (b) 3, (c) 4, (d) 6, Which of the following is the equation of a, circle ?, (a) x 2  2 y 2  x  6  0, , (c) x 2  y 2  5 x  0, 9., , (b) x 2  y 2  2 x  2 y  1  0, , (c) x 2  y 2  xy  1  0, 3., , (b) 1/ 2, , (a) 2, 4., , 5., , 6., , (c) x 2  y 2  2 x  2 y  1  0, 10., , (c) x  8, y  2, If, , (d) None of these, the, , (b) x 2  y 2  6 x  6 y  9  0, , (c) x 2  y 2  30 x  30 y  225  0, , 12., , (d) x 2  y 2  30 x  30 y  225  0, The equation of the circle with centre on x-axis,, radius 5 and passing through the point (2,3) is, (a) x 2  y 2  4 x  21  0, x 2  y 2  12 x  11  0, (b) x 2  y 2  4 x  21  0, x 2  y 2  12 x  11  0, (c) x 2  y 2  4 x  21  0, x 2  y 2  12 x  11  0, (d) x 2  y 2  5 x  21  0, x 2  y 2  12 x  11  0, Equation of line passing through mid point of, , 13., , (c) 3 x  4 y  12  0, (d) 3 x  2 y  6  0, The, intercepts, made, by, the, circle, , 11., , equation, , px  (2  q) xy  3 y  6qx  30 y  6q  0, 2, , 2, , represents a circle, then the values of p and q are, (a) 2,2, (b) 3,1, (c) 3,2, (d) 3,4, The, centres, of, the, circles, 2, 2, x  y  6 x  8 y  7  0 and, , x 2  y 2  4 x  10 y  3  0 are the ends of the, , diameter of the circle, , (a) x 2  y 2  5 x  9 y  26  0, (b) x  y  5 x  9 y  14  0, 2, , 2, , (c) x 2  y 2  5 x  y  14  0, 7., , (d) x 2  y 2  5 x  y  14  0, , The circle x 2  y 2  4 x  4 y  4  0, (a) touches x-axis only, (b) touches both axes, (c) passes through the origin, (d) touches y-axis only, , (d) x 2  y 2  2 x  2 y  1  0, The equation of a circle passing through (3,-6), and touching both the axes is, (a) x 2  y 2  6 x  6 y  9  0, , (c) 2, (d) 1 / 2, If ( x,3) and (3,5) are the extremities of a, diameter of a circle with centre at (2, y ). Then, the value of x and y are (a) x  1, y  4, (b) x  4, y  1, , (d) x 2  y 2  5 x  0, A circle touches both the axes and its centre lies, in the fourth quadrant. If its radius is 1 then its, equation will be (a) x 2  y 2  2 x  2 y  1  0, , (b) x 2  y 2  x  y  1  0, , (d) 3( x 2  y 2 )  5 x  1  0, The radius of the circle passing through the, points (0,0), (1,0) and (0,1) is -, , The equation of the circle passing through the, point (2,1) and touching y-axis at the origin is, , 14., , intercepts made by circle x 2  y 2  4 x  6 y  0, on co-ordinate axes is, (a) 3 x  2 y  12  0, (b) 3 x  y  6  0, , x 2  y 2  5 x  13 y  14  0 on the x-axis and y-, , axis are respectively, (a) 9,13, (b) 5,13, (c) 9,15, (d) none, The circle described on the line joining the, points (0,1), (a,b) as diameter cuts the x-axis in, points whose abscissa are roots of the equation:, (a) x 2  ax  b  0 (b) x 2  ax  b  0, (c) x 2  ax  b  0 (d) x 2  ax  b  0, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 1

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Circle, , JEE (Main+Advanced), 15., , The, , parametric equations, 4 x  4 y 2  25 is, 2, , of, , the, , (a) (4,3), , circle, , 5, 3, cos  , y  sin , 2, 2, 5, 5, (b) x  cos  , y  sin , 2, 2, 7, 7, (c) x  cos  , y  sin , 2, 2, 1, 1, (d) x  cos  , y  sin , 2, 2, , 23., , 25., , 17., , x 2  y 2  1, then  , (a) (1, 0), (b) ( 2, 0), (c) (3, 2), (d) (0, 2), The line 3 x  5 y  9  0 w.r.t., , 18., , (a) chord, (b) diameter, (c) tangent, (d) None, Circle x 2  y 2  4 x  8 y  5  0 will intersect, , (a) x , , 24., , Section (B) : Power and position of a point and line,, Tangents and normal, 16., The point   ,1    lines inside the circle, , 19., , 21., , (a) 10  m  5 (b) 9  m  20, (c) 35  m  15 (d) None of these, Find the co-ordinates of point, x  y  13, nearest, to, the, , x  y  4x  6 y  5  0, (a) ( 6, 7), (b) ( 15, 2), (c) ( 5, 6), (d) ( 7, 6), 2, , on, , circle, , 29, , (b), , x  y  25 at the point 2, , 2, , 26., , (a) 7, (c) 49, Find equation, , (b) 2 7, (d) 56, of tangent, , to, , the, , x  y  30 x  6 y  109  0 at (4,-1), (a) 11x  2 y  46  0, (b) 11x  2 y  46  0, (c) 11x  2 y  46  0, (d) 11x  3 y  46  0, 2, , 2, , circle, , The equation of a circle which touches both axes, and the line 3 x  4 y  8  0 and whose centre, lies in the third quadrant is, , (d) x 2  y 2  4 x  4 y  4  0, The, condition, so, that, , the, line, ( x  g ) cos   ( y  f ) sin   k is a tangent to, , x 2  y 2  2 gx  2 gx  2 fy  c  0 is, , (a) g 2  f 2  c  k 2, , (b) g 2  f 2  c 2  k, , (c) g 2  f 2  c 2  k 2, 27., , the, , x 2  y 2  6 x  8 y  0 is, , (c) x 2  y 2  4 x  4 y  4  0, , (d) g 2  f 2  c  k, The, tangent, lines, to, the, circle, 2, 2, x  y  6 x  4 y  12 which are parallel to the, line 4 x  3 y  5  0 are given by :, , (a) 4 x  3 y  7  0, 4 x  3 y  15  0, , (b) 4 x  3 y  31  0, 4 x  3 y  19  0, 28., , (c) 4 x  3 y  17  0, 4 x  3 y  13  0, (d) None of these, The tangent to the circle x 2  y 2  5 at the point, , (1, 2) also, , touches, , x  y  8 x  6 y  20  0 at, (a) ( 2,1), (b) (3, 0), (c) (1, 1), (d) (3, 1), , 38, , (c) 37, (d) 41, Line, 3 x  4 y  25 touches, , The length of chord x  y  1  0 w.r.t. circle, , (b) x 2  y 2  4 x  4 y  4  0, , line, circle, , (c) (12, 4), (d) None, Radius of the circle with centre (3,-1) and, cutting a chord of length 6 on the line, 2 x  5 y  18  0 is, , (d) None of these, , (a) x 2  y 2  4 x  4 y  4  0, , The co-ordinate of the point on the circle, x 2  y 2  12 x  4 y  30  0, which is farthest, from the origin are:, (a) (9,3), (b) (8,5), , (a), , 22., , 2, , the line 3 x  4 y  m in two distinct points, if -, , 2, , 20., , the, , x  y  4 x  6 y  5  0 is, 2, , (c) ( 3, 4), , (b) (3, 4), , 2, , circle, , 2, , the, , circle, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 2

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JEE (Main+Advanced), 29., , Circle, , The equation of the normal to the circle, x 2  y 2  2 x, which is parallel to the line, , x  2 y  3 is, (a) x  3 y  7, (c) x  2 y  2, , 30., , The, , equation, , (b) x  2 y  1, , (d) x  2 y  5, of normal to, , x  y  4 x  4 y  17  0 which, 2, , 2, , through (1,1) is, (a) 3 x  y  4  0 (b) x  y  0, , the, , circle, , passes, , (c) x  y  0, (d) None, The normal at the point (3,4) on a circle cuts the, circle at the point (-1,-2). Then the equation of, the circle is, (a) x 2  y 2  2 x  2 y  13  0, , 31., , 36., , (b) x 2  y 2  2 x  2 y  11  0, , 37., , (c) y  0, x  4, , 35., , (d) (h  r ) x  2rhy  0, x  0, The length of the tangent drawn from the point, (4,-1) to the circle 2 x 2  2 y 2  1 is, 2, , (a), , 17, 2, , 2, , (b), , If the length of tangent drawn from the point, (5,3) to the circle x 2  y 2  2 x  ky  17  0 is, 7, then k =, (a) -6, (b) -4, (c) 4, (d) 13/2, The length of the tangent drawn from any point, on the circle x 2  y 2  2 gx  2 fy  p  0 to the, , q p, , (a), 38., , 39., , 40., , 41., , 42., , pq, , (b), , q p, , (c), , (d) None, , Two perpendicular tangents to the circle, x 2  y 2  a 2 meet at P. Then the locus of P has, the equation (a) x 2  y 2  2a 2 (b) x 2  y 2  3a 2, (c) x 2  y 2  4a 2 (d) None of these, The angle between the two tangents from the, origin to the circle ( x  7)2  ( y  1) 2  25, equals, , (a), , (a) x  0, y  0, , (b) (h 2  r 2 ) x  2rhy  0, x  0, , 2, , (d), , circle x 2  y 2  2 gx  2 fy  q  0 is :, , (c) x 2  y 2  2 x  2 y  12  0, , (d) x 2  y 2  2 x  2 y  14  0, Section (C) : Pair of tangents (Joint equation and, length of tangent) Director circle, chord of contact,, chord with given middle point, and chord joining two, point, 32., The number of tangents that can be drawn from, the point (8,6) to the circle x 2  y 2  100  0 is, (a) 0, (b) 1, (c) 2, (d) None, 33., A line segment through a point P cuts a given, circle in 2 points A & B, such that PA = 16 &, PB = 9, then the length of tangent from point P, to the circle is, (a) 7, (b) 25, (c) 12, (d) None of these, 34., The equation of the tangents drawn from the, origin, to, the, circle, 2, 2, 2, x  y  2rx  2hy  h  0 are, , 33, 2, , (c), , (c), , , , (b), , 4, , , , , , 3, , (d) None, , 2, , The equation of the diameter of the circle, , ( x  2)2  ( y  1) 2  16 which bisects the chord, cut off by the circle on the line x  2 y  3  0 is, (a) x  2 y  0, (b) 2 x  y  3  0, (c) 3 x  2 y  4  0 (d) None, The co-ordinates of the middle point of the, chord cut off on 2 x  5 y  18  0 by the circle, , x 2  y 2  6 x  2 y  54  0 are, (a) (1, 4), (b) (2, 4), (c) (4,1), (d) (1,1), , The distance between the chords of contact of, tangents, to, the, circle, :, , x 2  y 2  2 gx  2 fy  c  0 from the origin &, , the point (g,f) is :, (a), , 33, , g f, 2, , 2, , (b), , g2  f 2  c, 2, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 3

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JEE (Main+Advanced), , (c), 43., , g2  f 2  c, , (d), , 2 g2  f 2, , g2  f 2  c, , 2 g2  f 2, , 49., , The locus of the mid point of a chord of the, circle x 2  y 2  4 which subtends a right angle, at the origin is :, (b) x 2  y 2  1, , (a) x  y  2, , 44., , Circle, , (c) x  y  2 (d) x  y  1, The locus of the centers of the circles such that, the point (2,3) is the mid point of the chord, 5 x  2 y  16 is :, 2, , 2, , (a) 2 x  5 y  11  0 (b) 2 x  5 y  11  0, , (c) 2 x  5 y  11  0 (d) None, Section (D) : Common tangents, common chord and, orthogonality, 45., Consider, the, circles, 2, 2, 2, 2, x  ( y  1)  9, ( x  1)  y  25. They are, such that (a) each of these circles lies outside the other, (b) one of these circles lies entirely inside the, other, (c) these circles touch each other, (d) they intersect in two points, 46., Number of common tangents of the circles, , ( x  2)  ( y  2)  49 and, 2, , 2, , 50., , 47., , 51., , x 2  y 2  6 x  18 y  26  0 at their point of, , contact is, (a) 12 x  5 y  19  0, , 52., , 53., , 54., , x 2  y 2  2 x  6 y  9  0 and, , x2  y2  6x  2 y  1  0, (a) x  0,3 x  4 y  10, y  4, 3 y  4 x, (b) x  0,3 x  4 y  10, y  4,3 y  4 x., , 55., , (b), , 15, , (c) 5, (d) 7, If the length of a common internal tangent to, two circles is 7, and that of a common external, tangent is 11, then the product of the radii of the, two circles is :, (a) 18, (b) 20, (c) 16, (d) 12, If the two circles, x 2  y 2  2 g1 x  2 f1 y  0 &, , x 2  y 2  2 g 2 x  2 f 2 y  0 touch, , (c) f1 f 2  g1 g 2, , (b), , each, , other, , f1 f 2, , g1 g 2, , (d) None, , If the circle C1 : x 2  y 2  16 intersects another, circle C2 of radius 5 in such a manner that the, common chord is of maximum length and has a, slope equal to 3/4, then the co-ordinates of the, centre of C2 are :, ,  9 12 , ,  5 5,  12 9 , (c)   ,  ,  5 5, (a)   , , , (d) 12 x  5 y  19  0, Find the equations to the common tangents of, circles, , 14, , (a) f1 g1  f 2 g 2, , (c) 5 x  12 y  19  0, the, , ( x  1)2  ( y  2) 2  4 and, , circle, , then:, , (b) 5 x  12 y  19  0, 48., , (b) 192, , (c) 25, (d) 250, Find the length of direct common tangent of, , (a), , 2, , x 2  y 2  4 x  6 y  12  0 and, , 192, 25, , ( x  5) 2  ( y  2) 2  1, , (a) 0, (b) 1, (c) 2, (d) 3, The equation of the common tangent to the, circle, , from the point (4,3) to the circle x 2  y 2  9 and, the line joining their point of contact is :, , (a), , ( x  2)  ( y  1)  4 is :, 2, , (d) x  0,3 x  4 y  10, y  4,3 y  4 x  0, The angle of intersection of two circles is 00 if (a) they are separate, (b) they intersect at two points, (c) they intersect only at a single point, (d) it is not possible, The area of the triangle formed by the tangents, ,  9 12 , , 5,  5,  12 9 , (d)   ,  , 5,  5, , (b)   , , , The locus of the centre of the circle which, bisects the circumferences of the circles, , x 2  y 2  4 & x 2  y 2  2 x  6 y  1  0 is :, , (c) x  0,3x  4 y  10, y  4, 3 y  4 x  0, , (a) a straight line (b) a circle, (c) a parabola, (d) none of these, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 4

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Circle, , JEE (Main+Advanced), 56., , Two circles whose radii are equal to 4 and 8, intersect at right angles. The length of their of, their common chord is :, , 16, (a), 5, , 57., , 58., , (c) 4 6, , The, , (b) 8, , (d), , circumference, , 8 5, 5, , of, , the, , 3, (c) 2 or, 2, , 3, 2, , 63., , (b) -2 or , , 2 x 2  2 y 2  4 x  7 y  25  0 and point (1,1) is, , (a) 4 x 2  4 y 2  30 x  10 y  25  0, , 3, (d) -2 or, 2, , (b) 4 x 2  4 y 2  30 x  13 y  25  0, , orthogonally,, , 3, 2, , circles, , (c) 4 x 2  4 y 2  17 x  10 y  25  0, 64., , (b) x 2  y 2  5 x  5 y  8  0, (c) x 2  y 2  5 x  5 y  8  0, , x 2  y 2  5 x  5 y  9  0, and, , (a) x 2  y 2  16 x  18 y  4  0, (b) x 2  y 2  7 x  11 y  6  0, , 60., , (d) 4 x 2  4 y 2  30 x  13 y  25  0, Find equation of circle passing through the point, (4,4) and touching the line x  y  2  0 at (1,1), (a) x 2  y 2  5 x  5 y  8  0, , x 2  y 2  2 x  3 y  7  0,, , x 2  y 2  7 x  9 y  29  0 is, , (c) x 2  y 2  5 x  2 y  72  0, (d) none of these, The equation of a circle passing through points, of, intersection, of, the, circle, , x 2  y 2  13 x  3 y  0 and, , Equation of the circle cutting orthogonally the, three, , x 2  y 2  2 x  3 y  5  0 in A & B. Then the, , (b) 9( x 2  y 2 )  8 x  4 y  25  0, , x 2  y 2  2 x  2ky  6  0 and, , x 2  y 2  2ky  k  0 intersect, , (a) 2 or , , circle, , equation of the circle on AB as a diameter is :, , circle, , circle x 2  y 2  4 x  12 y  p  0, then p  q is, equal to :, (a) 25, (b) 100, (c) 10, (d) 48, , If the circles, , (d) none of these, x  y 2  4 cuts the, 2, , (a) 13( x 2  y 2 )  4 x  6 y  50  0, , x 2  y 2  2 x  8 y  q  0 is bisected by the, , then k is, , 59., , 62., , (c) a parabola, The circle, , 65., , (c) x 2  y 2  2 x  8 y  9  0, (d) None of these, The equation of the circle which passes through, the origin has its centre on the line x  y  4, , (d) x 2  y 2  5 x  5 y  8  0, Find equation of circle passing through the, points (1,1) and (3,3) and whose centre line an, x-axis, (a) x 2  y 2  8 x  6  0, (b) x 2  y 2  8 x  6  0, (c) x 2  y 2  8 x  6  0, , (d) x 2  y 2  8 x  8  0, , and cuts the circle x 2  y 2  4 x  2 y  4  0, orthogonally, is -, , (a) x 2  y 2  2 x  6 y  0, (b) x 2  y 2  6 x  3 y  0, , (c) x 2  y 2  4 x  4 y  0, (d) None of these, Section (E) : Radical axis and family of circle, 61., The locus of the centre of the circle which, bisects the circumferences of the circles, , x 2  y 2  4 & x 2  y 2  2 x  6 y  1  0 is :, , (a) a straight line (b) a circle, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 5

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Circle, , JEE (Main+Advanced), , Answer Key, 1, d, 11, a, 21, b, 31, b, 41, a, 51, b, 61, a, , 2, d, 12, d, 22, b, 32, b, 42, c, 52, a, 62, a, , 3, b, 13, c, 23, b, 33, c, 43, c, 53, b, 63, b, , 4, a, 14, b, 24, b, 34, b, 44, a, 54, b, 64, b, , 5, c, 15, b, 25, c, 35, c, 45, b, 55, a, 65, c, , 6, a, 16, a, 26, a, 36, b, 46, b, 56, a, , 7, b, 17, b, 27, b, 37, a, 47, b, 57, c, , 8, b, 18, c, 28, d, 38, a, 48, a, 58, a, , 9, a, 19, a, 29, b, 39, c, 49, c, 59, a, , 10, a, 20, a, 30, a, 40, b, 50, a, 60, c, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 6