Hyperbola Test ...

Equation of the common tangent to y² = 8x and 3x² - y² = 3 is

The equations of the common tangents to the two hyperbolas  and 

If the tangent at the point (h, k) on the hyperbola  meets the auxiallary circle of the hyperbola in two points whose ordinates y₁, y₂ then 

If x = 9 is the chord of contact of the hyperbola x² - y² = 9, then the equation of the tangent at one of the points of contact is 

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

The mid-point of the chord 4x – 3y = 5 of the hyperbola 2x² - 3y² = 12 is

The equation of the transverse and conjugate axes of a hyperbola are respectively x + 2y – 3 = 0, 2x – y + 4 = 0 and their respective lengths are √2 and 2/√3. The equation of the hyperbola is

If two distinct tangents can be drawn from the point (α²) on different branches of the hyperbola 

A hyperbola has centre C and one focus at P(6, 8). If its two directrices are 3x + 4y + 10 = 0 and 3x + 4y -10 = 0 then CP =

A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x² + 4y² = 12. Then its equation is: