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

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

If the foci of the ellipse  and the hyperbola  conincide, then the value of b² is

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

 touches the hyperbola x² – 2y² = 4, then the point of contact is

Equation of tangent to the hyperbola 2x² – 3y² = 6 which is parallel to the line y = 3x + 4 is

Let , be two points on the hyperbola . If (h, k) is thepoint of intersection of the normal’s at P and Q, k is equal to

Let , be two points on the hyperbola . If (h, k) is thepoint of intersection of the normal’s at P and Q, k is equal to