Tangents at any point P is drawn to hyperbola `(x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1` intersects asymptotes at Q and R, if O is the centre of hyperbola then

A tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its asymptotes at P and Q. If C its centre,prove that CP.CQ=a^(2)+b^(2)

The tangent at any point P on a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C meets the assymptotes is bisected at the point of contact . This implies that the locus of the centre of the circle circumscribing Delta CQR in case of a rectangular hyperbola is the hyperbola itself.

Tangents at any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cut the axes at A and B respectively,If the rectangle at OAPB (where O is origin) is completed then locus of point P is given by

Point P, Q and R on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 are such that line PQ passes through the centre of the hyperbola . Then product of slopes of PR and QR is

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If these tangents cut the coordinates axes at 4 concyclic points, then the locus of P is

From a point P, two tangents PA and PB are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the product of the slopes of these tangents is 1, then the locus of P is a conic whose eccentricity is equal to

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then