Question 1 : The locus of the point which moves such that the ratio of its distance from two fixed point in the plane is always a constant <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7bc22399925718ac6a20c"> is
Question 2 :
The length of the latusrectum of the parabola whose focus is (3,3) and directrix is 3x-4y-2=0 is
Question 3 : Consider the hyperbola <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749bd546f7eb01d9e6d7a4' height='43' width='76' > the area of the triangle formed by the asymptotes and the tangent drawn to it at (a, 0) is
Question 4 :
A parabola has the origin as its focus and the line x=2 as the directrix. Then the vertex of the parabola is at
Question 5 :
The number of tangent which can be drawn from the point (-1, 2) to the circle x<sup>2</sup> + y<sup>2</sup> + 2x- 4y + 4 = 0 is -
Question 6 :
If y<sub>1</sub>, y<sub>2</sub> are the ordinates of two points P and Q on the parabola and y<sub>3</sub> is the ordinate of the point of intersection of tangents at P and Q, then
Question 7 :
The normal at (16,16) to the parabola y<sup>2</sup> = 16x again meets at
Question 8 :
The curve represented by x = a(cos hθ + sin hθ), y = b (cos hθ - sin hθ) is
Question 9 :
ax<sup>2</sup> + 2bxy + 2y<sup>2</sup> - 8x - 12y - 6 = 0 represents a circle if
Question 10 :
The value of P such that the vertex of y = x<sup>2</sup> + 2px + 13 is 4 <br>unit above the x axis is -
Question 11 :
Equation of circle touching lines | x - 1| + |y + 2| = 2 is
Question 12 :
If the line lx + my = 1 be a tangent to the circle x<sup>2</sup> + y<sup>2</sup> = a<sup>2</sup>, then the locus of the point (l, m) is-
Question 13 :
If the chord y = mx + 1 subtends an angle of measure 45<sup>0</sup> at the major segment of the circle x<sup>2</sup> + y<sup>2</sup> = 1 then value of m is-
Question 15 :
The normal to the rectangular hyperbola xy = c<sup>2</sup> at the point 't' meets the curve again at a point 't' such that
Question 16 :
A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP<sup>2</sup> + CQ<sup>2</sup> + CR<sup>2</sup> + CS<sup>2</sup> is equal to
Question 17 :
The name of the conic represented by the equation x<sup>2</sup> + y<sup>2</sup> - 2xy + 20x + 10 = 0 is-
Question 18 :
The number of points with integral coordinates that lie in the interior of the region common to the circle x<sup>2</sup> + y<sup>2</sup> = 16 and the parabola y<sup>2</sup> = 4x is -
Question 19 : If the line lx + my + n = 0 meets the hyperbola <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749ab346f7eb01d9e6d655' height='41' width='52' > = 1 at the extremities of a pair of conjugate diameters, then the relation a<sup>2</sup> - b<sup>2</sup>m<sup>2</sup> is equal to -
Question 20 :
The abcissa and ordinate of the end points A and B of a focal chord of the parabola y<sup>2</sup> = 4x are respectively the roots of x<sup>2</sup> - 3x + a = 0 and y<sup>2</sup> + 6y + b = 0. The equation of the circle with AB as diameter is.
Question 21 :
If the chord of contact of tangents from a point P to the parabola y<sup>2</sup> = 4ax, touches the parabola x<sup>2</sup> = 4by, then the locus of P is a/an -
Question 22 :
The angle between the asymptotes of the hyperbola 3x<sup>2</sup> − y<sup>2</sup> = 3 is
Question 23 :
The equation of the hyperbola whose vertices are at (5, 0) and ( − 5, 0) and one of the directrices is $x = \frac{25}{7},$ is
Question 24 :
The length of the latusrectum of an ellipse is one third of its major axis. Its eccentricity would be
