If any tangent to the ellipse makes intercepts of lengths p and q on the axes, prove that `(a^(2))/(p^(2))+(b^(2))/(q^(2))=1`

Line L has intercepts a and b on the axes of co ordinates. When the axes are rotated through a givenn angle, keeping the origin fixed, the straight line L has intercpets p and q on the transformed axes. Prove that 1/(a^(2))+1/(b^(2))=1/(p^(2))+1/(q^(2)) .

If any tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 intercepts equal length l on the axes then l =

The tangent at any point P on the ellipse meets the tangents at the vertices A & A^(1) of the ellipse (x^(2))/(a^(2))+( y^(2))/(b^(2))=1 at L and M respectively. a b Then AL. A^(1) M =

If the tangent at any point on the curve ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1 makes the intercepts, p,q and the axes then (p^(2))/(a^(2))+(q^(2))/(b^(2))=

Find the equation of the chord joining point P(alpha) and Q(beta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.

Two system of rectangular cartesian coordinate axes have the same origin. If a plane cuts them at distance a, b, c and p, q, r from the origin, the show that (1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))=(1)/(p^(2))+(1)/(q^(2))+(1)/(r^(2)) .

The least intercept made by the coordinate axes on a tangent to the ellipse (x^(2))/(64)+(y^(2))/(49)=1 is