A tangent to the ellipse `( x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 ` meets the ellipse ` (x^(2))/(a^(2)) + (y^(2))/( b^(2)) = a + b` in the points P and Q , prove that the tangents at P and Q are at right angles

A tangent is drawn to the ellipse to cut the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and to cut the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 at the points P and Q. If the tangents are at right angles,then the value of ((a^(2))/(c^(2)))+((b^(2))/(d^(2))) is

A tangent is drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to cut the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 at the points P and Q . If tangents at P and Q to the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect at right angle then prove that (a^(2))/(c^(2))+(b^(2))/(d^(2))=1

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is

If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes intercepts p and q on the coordinate axes, then a^(2)/p^(2) + b^(2)/q^(2) =

A tangent to the ellipse x^(2)+4y^(2)=4 meets the ellipse x^(2)+2y^(2)=6 at P o* Q.

If 3x+4y=12 intersect the ellipse (x^(2))/(25)+(y^(2))/(16)=1 at P and Q, then point of intersection of tangents at P and Q.

A variable tangent to the circle x^(2)+y^(2)=1 intersects the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at point P and Q. The lous of the point of the intersection of tangents to the ellipse at P and Q is another ellipse. Then find its eccentricity.

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is

Tangents,one to each of the ellipses (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 are drawn Tangents,If the tangents meet at right angles then the locus of their point of intersection is