Question

A tangent to the parabola x² = 4ay meets the hyperbola xy = k² in two points P and Q. Then the middle point of PQ lies on a:

• A. Circle
• B. A parabola
• C. An ellipse
• D. Hyperbola

Answer 1

Answer: (B)

A parabola

Answer 2

Let (a, b) be the middle points.

\ Equation of chord bisected is S₁ = T

Ž y = $\frac { - \alpha } { \beta }$+ 2a which is tangent to

x² = 4a

where D = 0

Ž b² = or, y²

= – (which is parabola)