A tangent to the ellipse `x^2/9+y^2/4=1` with centre `C` meets is director circle at `P` and `Q.` Then the product of the slopes of `CP` and `CQ,` is

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.

A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&Q.

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

If a tangent to the ellipse x^2/a^2+y^2/b^2=1 , whose centre is C, meets the major and the minor axes at P and Q respectively then a^2/(CP^2)+b^2/(CQ^2) is equal to

If the tangent to the ellipse x^(2)+2y^(2)=1 at point P((1)/(sqrt(2)),(1)/(2)) meets the auxiliary circle at point R and Q, then find the points of intersection of tangents to the circle at Q and R.

If a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose centre is C, meets the major and the minor axes at P and Q respectively then (a^(2))/(CP^(2))+(b^(2))/(CQ^(2)) is equal to

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

A tangent to the circle x^(2)+y^(2)=4 meets the coordinate axes at P and Q. The locus of midpoint of PQ is