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

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

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

If any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C, meets its director circle in P and Q, show that CP and CQ are conjugate semi-diameters of the hyperbola.

If any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C, meets its director circle in P and Q, show that CP and CQ are conjugate semi-diameters of the hyperbola.

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

If two points P & Q on the hyperbola , x^2/a^2-y^2/b^2=1 whose centre is C be such that CP is perpendicularal to CQ and a lt b 1 ,then prove that 1/(CP^2)+1/(CQ^2)=1/a^2-1/b^2 .