Let two points P and Q lie on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`,
whose centre C be such that CP is perpendicular to CQ,
a lt b. Then the value of `(1)/(CP^(2))+(1)/(CQ^(2))` 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 .

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 .

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the value of (1)/(y_(1))+(1)/(y_(2)) is

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

The tangents from P to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are mutually perpendicular show that the locus of P is the circle x^(2)+y^(2)=a^(2)-b^(2)

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 point of intersection of two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , the product of whose slopes is c^(2) , lies on the curve

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

Find the equations of the tangents to the hyperbola (x ^(2))/(a ^(2)) - (y ^(2))/( b ^(2)) = 1 are mutually perpendicular, show that the locus of P is the circle x ^(2) + y ^(2) =a ^(2) -b ^(2).

For the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , distance between the foci is 10 units. Form the point (2, sqrt3) , perpendicular tangents are drawn to the hyperbola, then the value of |(b)/(a)| is