Show that the tangents drawn at those points of the ellipse `(x^(2))/(a)+(y^(2))/(b)=(a+b)`, where it is cut by any tangent to `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`, intersect at right angles.

If the tangents drawn from a point (1,2 sqrt(3)) to the ellipse (x^(2))/(9)+(y^(2))/(b^(2))=1 are at right angles then b =

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

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

Tangents are drawn to the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =a+ b at the points where it is cut by the line (x)/(a^(2)) cos theta - ( y)/(b^(2)) sin theta =1 , then the point of intersection of Tangents

Show that the tangents at the end of any focal chord of the ellipse x^(2)b^(2)+y^(2)a^(2)=a^(2)b^(2) intersect on the directrix.

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