Hyperbola Test ...

The equation to the common tangents to the two hyperbolas  and  are

Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola 16y² – 9x² = 1 is

The ellipse 4x² + 9y² = 36 and the hyperbola 4x² – y² = 4 have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is

The equation of the common tangent to the parabola y² = 8x and the hyperbola 3x²– y² = 3 is

Equation of the chord of the hyperbola 25x² – 16y² = 400 which is bisected at the point (6, 2) is

The asymptotes of the hyperbola xy–3x–2y = 0 are

If the product of the perpendicular distances from any point on the hyperbola  of eccentricity e = √3 on its asymptotes is equal to 6, then the length of the transverse axis of the hyperbola is

If the normal to the rectangular hyperbola xy = c² at the point `t' meets the curve again at `t₁' then t³t₁ has the value equal to

Area of triangle formed by tangent to the hyperbola xy = 16 at (16, 1) and co-ordinate axes equals

Locus of the middle points of the parallel chords with gradient m of the rectangular hyperbola xy = c² is