If a tangent to the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` makes intercepts h and k on the co-ordinate axes then show that `a^(2)/h^(2)+b^(2)/k^(2)=1`.

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

If a chord of a the circle x^(2)+y^(2) = 32 makes equal intercepts of length of l on the co-ordinate axes, then

If 4x+y+k=0 is a tangent to the ellipse x^(2)+3y^(2)=3 then k = ?

(1) Draw the rough sketch of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 . Find the area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 .

Prove that the chords of constant of perpendicular tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touch another fixed ellipse (x^(2))/(a^(4))+(y^(2))/(b^(4))=(1)/((a^(2)+b^(2)))

The sum of the squares of the perpendiculars on any tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from two points on the minor axis each at a distance a e from the center is 2a^2 (b) 2b^2 (c) a^2+b^2 a^2-b^2

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

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

If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles alphaa n dbeta with the major axis such that tanalpha+tanbeta=gamma, then the locus of their point of intersection is (a) x^2+y^2=a^2 (b) x^2+y^2=b^2 (c) x^2-a^2=2lambdax y (d) lambda(x^2-a^2)=2x y