List of top Mathematics Questions on Hyperbola asked in JEE Main

A hyperbola, having the transverse axis of length $2 \, \sin \, \theta$ is confocal with the ellipse $3x^2 + 4y^2 = 12$. Its equation is

The locus of the point of intersection of the lines, $\sqrt{2} x-y + 4 \sqrt{2} \, k=0$ and $\sqrt{2} k x+k \, y-4 \sqrt{2} = 0$ (k is any non-zero real parameter), is :

$PQ$ and $RS$ are two perpendicular chords of the rectangular hyperbola $xy=c^2$. If $C$ is the centre of the rectangular hyperbola, then the product of the slopes of $CP,CQ,CR$ and $CS$ is equal to:

For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2}=1, C_1$ is a circle touching hyperbola having centre at origin and $C_2$ is circle centred at four and touching hyperbola at vertices, if area of $C_1= 36π$ and area of $C_2 = 4π$. Find $a_2 + b_2 $= ?