List of top Mathematics Questions on Conic sections asked in JEE Advanced

Let $ABCD$ be a quadrilateral with area 18, with side AB parallel to the side $CD$ and $AB = 2 CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides, then its radius is

If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is

If the line $2x+\sqrt6y=2$ touches the hyperbola $x^2-2y^2=4$, then the point of contact is

If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord to the circle with centre (2,1), then the radius of the circle is

The centre of circle inscribed in square formed by the lines $x^2 - 8x + 12 = 0$ and $y^2 - 14y + 45 = 0$, is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

Let AB be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then, the locus of the centroid of the $\Delta PAB$ as P moves on the circle, is

If two distinct chords, drawn from the point (p, q) on the circle $x^2 + y^2 = px + qy$ (where, $ pq \ne 0$) are bisected by the X-axis, then

If $P = (x, y),F_1 = (3,0), F_2 = ( 3, 0)$ and $ 16x^2 + 25y^2 = 400,$ then $PF_1 + PF_2$ equals

The locus of the centre of a circle, which touches externally the circle $x^2 + y^2 -6 x - 6y + 14 = 0$ and also touches the Y-axis, is given by the equation

The centre of a circle passing through the points $ (0, 0),(1, 0)$ and touching the circle $x^2 + y^2 = 9$ is

The lines $2x - 3y = 5$ and $3x - 4y = 7$ are diameters of a circle of area 154 sq unitis. Then, the equation of this circle is

The equations of the tangents drawn from the origin to the circle $x^2 + y^2 + 2 rx + 2hy + h^2 = 0, $ are

The equation of the circle passing through (1, 1) and the points of intersection of $x^2 + y^2 + 13x - 3y =0$ and $2x^2 + 2y^2 + 4 x - 7y -2 5 = 0$ is

The centre of the circle passing through the point (0, 1)and touching the curve $y = x^2 at (2,4)$ is

AB is a diameter of a circle and C is any point on the circumference of the circle. Then,

The equation $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents

Two circles $ x^2 + y^2 = 6$ and $ x^2 + y^2 - 6x + 8 = 0$ are given. Then the equation of the circle passing through their points of intersection and the point (1, 1) is