Hyperbola Test ...

If the equation 4x² + ky² = 18 represents a rectangular hyperbola, then k =

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy = c²

The asymptotes of the hyperbola hx + ky = xy are

The equation of a line passing through the centre of a rectangular hyperbola is x – y –1 = 0. if one of its asymptote is 3x-4y-6 = 0, then equation of its other asymptote is

Tangents are drawn to 3x² - 2y² = 6 from a point P. If these tangents intersects the coordinate axes at concyclic points, The locus of P is

If the curve  cut each other orthogonally then 

Let a and b be non–zero real numbers. Then, the equation (ax² + by² + (C) (x² – 5xy + 6y²) = 0 represents 

The asymptotes of the curve 2x² + 5xy + 2y² + 4x + 5y = 0 are given by

A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis is

If the vertex of a hyperbola bisects the distance between its centere and the corresponding focus, then ratio of square of its conjugate axis of the square of its transverse axis is