Question

If tangents PQ and PR are drawn from point P to $\frac{x^{2}}{a^{2}}$–$\frac{y^{2}}{b^{2}}$= 1 (a > b); so that fourth vertex S of parallelogram PQSR lie on circumcircle of triangle PQR, then locus of P is-

• A. x² + y² = b²
• B. x² + y² = a²
• C. x² + y² = a² – b²
• D. None of these

Answer 1

Answer: (C)

x² + y² = a² – b²

Answer 2

Fourth vertex lies on circumcircle

\ parallelogram is cyclic.

Ž parallelogram is rectangle.

and tangents are perpendicular.

So locus is director circle.