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`

Find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

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 .

The area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 is equal to

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

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

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

If the line y=mx+c is a tangent to the ellipse x^(2)+2y^(2)=4 , find c

Find the locus of point P such that the tangents drawn from it to the given ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meet the coordinate axes at concyclic points.

Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and a concentric circle of radius rdot

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.