If m is A Variable, The Locus Of The Point Of Intersection Of The Lines  is a/an 

A, B, C are three points on the rectangular hyperbola xy = c², find

1. The area of the triangle ABC

2. The area of the triangle formed by the tangents at A, B and C. 

Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola xy = c².

Find the equation of the hyperbola whose asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and which passes through the point

(1,–1 ). Find also the equation of the conjugate of the conjugate hyperbola.

The vertices of the hyperbola

The centre of the hyperbola

The eccentricity of the hyperbola with latusrectum 12 and semi-conjugate axis , is 

The equation of the hyperbola with vertices (3, 0) and (–3, 0) and semi-latusrectum 4, is given by

The equation of the tangent to the curve 4x² – 9y² = 1 which is parallel to 4y = 5x + 7, is

The equation of the tangent parallel to y = x drawn to  is

If the chords of contact of tangents from two points (x₁, y₁) and (x₂, y₂) to the hyperbola  are at right angles, then  is equal to