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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , CIRCLE, , PRACTICE EXERCISE 11.1, Q 1. Find the centre and radius of each of the following circles:, (i) x2 + y2- 4x + by = 5, (ii) x2 + y2 - x + 2y-3 = 0., 1. (i) (2, -3); 3√2 (ii), , , −1 ;, , √, , Q 2. Find the equation of the circle which passes through the point of intersection of the, lines 3 x – 2 y – 1 = 0 and 4 x + y – 27 = 0 and whose centre is (2, – 3)., 2. x2 + y2 – 4x + 6y – 96 = 0, Q 3. If the equations of the two diameters of a circle are x – y = 5 and 2x + y = 4 and the, radius of the circle is 5, find the equation of the circle., 3. x2 + y2 – 6x + 4y – 12 = 0, Q 4. Find the equation of the circle passing through the points (1, –2) and (4, –3) and whose, centre lies on the line 3x +4y = 7., 2, , 2, , 47  , 3  1465, , 4.  x     y   , 15  , 5, 225, , , Q 5. Find the equation of a circle of radius 5 whose centre lies on x–axis and passes through, the point (2, 3)., 5. x2 + y2 – 12x + 11 = 0 and x2 + y2 + 4x – 21 = 0, Q 6. If the equations of two diameters of a circle are 2x + y - 6 and 3x + 2y - 4 and the radius, is 10, find the equation of the circle., 6. x2 + y2 - 16x + 20y + 64 = 0, Q 7. Find the equation of the circle which touches:, (i) the x–axis and whose centre is (3, 4), (ii) both the axes and whose radius is 5, 7. (i) x2 + y2 – 6x – 8y + 9 = 0, (ii) x2 + y2 – 10x – 10y + 25 = 0, Q 8. Find the equation of a circle, (i) which touches both the axes at a distance of 6 units from the origin., (ii) which touches x-axis at a distance 5 from the origin and radius 6 units, (iii) which touches both the axes and passes through the point (2,1)., (iv) passing through the origin, radius 17 and ordinate of the centre is -15., 8. (i) x2 + y2 - 12x - 12y + 36 = 0 (ii) x2 + y2 - 10x - 12y + 25 = 0, (iii) x2 + y2 - 2x - 2y + 1 = 0, x2 + y2 - 10x - 10y + 25 = 0 (iv) x2 + y2 ± 16x + 30y = 0, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 1

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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , CIRCLE, , Q 9. A circle of radius 2 lies in the first quadrant and touches both the axes. Find the, equations of the circle with centre at (6, 5) and touching the above circle externally., 9. (x – 6)2 + (y – 5)2 = 32, Q 10. Find the equation of the circle which touches the coordinate axes and whose centre, lies on the line x – 2y = 3., 10. (x – 1)2 + (y + 1)2 = 12, Q.11 Find the equation of the circle passing through the point of intersection of the lines x +, 3y = 0 and 2x - 7y = 0 and whose centre is the point of intersection of the lines x - y + 1 = 0, and x - 2y + 4 = 0., 11. x2 + y2 + 4x - 2y = 0, Q 12. A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the, equations of its images with respect to the line mirrors x = 0 and y = 0., 12. With respect to x = 0; x2 + y2 + 8x - 8y + 16 = 0 With respect to y = 0 x2 + y2 - 8x + By, + 16 = 0, Q 13. One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the, coordinates of A and B are (- 3, 4) and (5, 4) respectively, find the equation of the circle., 13. x2 + y2 - 2x - 4y - 15 = 0, Q 14. Find the equation of the circle whose centre is (3, - 1) and which cut-off an intercept of, length 6 from the line 2x - 5y + 18 = 0., 14. x2 + y2 - 6x + 2y - 28 = 0, Q 15. Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8, units on the X-axis., 15. x2 + y2 ± 10x - 6y + 9 = 0, Q.16 Find the centre and radius of the circle x2 + y2 – 6x + 4y – 12 = 0., 16.Center = (3, -2) and Radius = 5, Q.17 Find the equation of the circle which passes through the points (5, – 8), (2, – 9) and (2,, 1). Find also the coordinates of its centre and radius., 17. x2 + y2 – 4x + 8y – 5 = 0, Centre = (2, -4) and Radius = 5, Q.18 Find the equation of the circle whose centre is at the point (4, 5) and which passes, through the centre of the circle x2 + y2 – 6x + 4y – 12 = 0., 18. x2 + y2 – 8x – 10y – 9 = 0, 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 2

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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , CIRCLE, , Q.19 Find the area of an equilateral triangle inscribed in the circle x 2 + y2 + 2gx + 2fy + c =, 0., 19., , 3 3 2, (g  f 2  c) sq. units, 4, , Q.20 Find the equation of the circle that passes through the point (1, 0), (–1, 0) and (0, 1)., 20. x2 + y2 = 1, Q.21 The straight line, , x y,   1 cuts the coordinate axes at A and B. Find the equation of, a b, , the circle passing through O (0, 0), A and B., 21. x2 + y2 – ax – by = 0, Q.22 Find the equation of the circle passing through (1, 0) and (0, 1) and having the smallest, possible radius., 22. x2 + y2 – x – y = 0, Q.23 Show that the points (9, 1), (7, 9) (–2, 12) and (6, 10) are concyclic., Q.24 Find the coordinates of the centre and radius of each of the following circles :, (i) l/2(x2 + y2) + x cos  + y sin  - 4 = 0, (ii) x2 + y2 - ax - by = 0, 24. (i) (- cos , - sin ); 3, (ii) , ; √𝑎 + 𝑏, Q.25 Find the equation of the circle passing through the points:, (i) (5, 7), (8, 1) and (1, 3), (ii) (1, 2), (3, - 4) and (5. - 6), (iii) (5, - 8), (- 2, 9) and (2, 1), (iv) (0, 0), (- 2,1 ) and (- 3, 2), 2, 2, 25. (i) 3(x + y ) - 29x - 19y + 56 = 0, (ii) .x2 + y2 - 22x - 4y + 25 = 0, (iii) x2 + y2 + 116x + 48y - 285 = 0, (iv) x2 + y2 - 3x - 11y = 0, Q.26 Find the equation of the circle which passes through (3, -2), (-2, 0) and has its centre, on the line 2x - y = 3., 26. x2 + y2 + 3x + 12y + 2 = 0, Q.27 Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its, centre on the line x - 4y = 1., 27. x2 + y2 + 6x + 2y-90 = 0, Q.28 Show that the points (3, - 2), (1, 0), (- 1, - 2) and (1, - 4) are concyclic., Q.29 Show that the points (5, 5), (6, 4), (-2, 4) and (7, 1) all lie on a circle, and find its, equation, centre and radius., 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 3

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M.K. MATHEMATICS (M.:8826181724), , CLASS:-XI, , CIRCLE, , Q.30 Find the equation of the circle concentric with x2 + y2 - 4.x- 6y - 3 = 0 and which, touches the y-axis., 30. x2 + y2 - 4x - 6y + 9 = 0, Q.31 Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose, radius is 1. Show that there are two such circles., 31. x2 + y2 - 4x - 2y + 4 = 0, x2 + y2 - 2x - 4y + 4 = 0, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK 2nd FLOOR, , Page 4