If The Foci Of The Ellipse  and The Hyperbola  conincide, Then The Value Of b2 is

If (asecθ, btanθ) and (asecÏ•, btanÏ•) are the ends of a focal chord of  equal to

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

The point of intersection of the curves whose parametric equation are x = t² + 1, y = 2t and x = 2s, y = 2/s, is given by

The area of triangle formed by the lines x – y = 0, x + y = 0 and any tangent to the hyperbola x²  – y² = a² is

A circle cuts the rectangular hyperbola xy = 1 in the points (x_r, y_r),r = 1, 2, 3, 4. Then the values of x₁x₂x₃x₄ and y₁y­₂y₃y₄ respectively, are

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

If e and e’ be the eccentricities of two conics S and S’ such that e² + e’² = 3, then both S and S’ are

The eccentricity of the hyperbola 2x² – y² = 4 is

Which one of the following is independent of  in the hyperbola .

Consider a branch of the hyperbola  with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is