If tangents PQ and PR are drawn from variable point P to the hyperbola x2a2−y2b2=1(a>b) so that the fourth vertex S of parallelogram PQSR lies on circumcircle of triangle PQR, then locus of P is

PQRS are concyclic points Fourth vertex S lies on circle∴Tangents are perpendicular⇒P lies on director circle⇒Locus of P is x2+y2=a2−b2

If tangents PQ and PR are drawn from variable point P to the hyperbola x2a2−y2b2=1(a>b) so that the fourth vertex S of parallelogram PQSR lies on circumcircle of triangle PQR, then locus of P is

PQRS are concyclic points Fourth vertex S lies on circle∴Tangents are perpendicular⇒P lies on director circle⇒Locus of P is x2+y2=a2−b2

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

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$x^{2} + y^{2} = b^{2}$

$x^{2} + y^{2} = a^{2}$

$x^{2} + y^{2} = (a^{2} - b^{2})$

$x^{2} + y^{2} = a^{2} + b^{2}$

answer is C.

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PQRS are concyclic points Fourth vertex S lies on circle
$∴$ Tangents are perpendicular
$\Rightarrow$ P lies on director circle
$\Rightarrow$ Locus of P is $x^{2} + y^{2} = a^{2} - b^{2}$

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If tangents PQ and PR are drawn from variable point P to the hyperbola x2a2−y2b2=1(a>b) so that the fourth vertex S of parallelogram PQSR lies on circumcircle of triangle PQR, then locus of P is

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