Length of the focal chord of the ellipse `x^2/a^2+y^2/b^2= 1` which is inclined to the major axis at angle `theta` is

Show that the length of the focal chords of ellipse x^2/a^2 + y^2/b^2 = 1 which makes an angle theta with the major axis is (2ab^2)/(b^2 cos^2 theta + a^2 sin^2 theta) unit

The locus of mid-points of a focal chord of the ellipse x^2/a^2+y^2/b^2=1

Length of the major axis of the ellipse 9x^(2)+7y^(2)=63, is

The locus of the mid-points of the chords of the ellipse x^2/a^2+y^2/b^2 =1 which pass through the positive end of major axis, is.

The locus of mid point of focal chords of ellipse x^2 / a^2 +y^2/b^2 =1

A circle of radius r is concentric with the ellipse x^2/a^2 + y^2/b^2 = 1 . Prove that the common tangent is inclined to the major axis at an angle tan^(-1) sqrt((r^2-b^2)/(a^2 - r^2) .

The equation of the chord of the ellipse 2x^2+ 5y^2 =20 which is bisected at the point (2, 1) is

The equation of the chord of the ellipse 2x^2+ 5y^2 =20 which is bisected at the point (2, 1) is

The length of the major axis of the ellipse 3x^2+2y^2-6x8y-1=0 is

If the tangent at any point of the ellipse (x^2)/(a^3)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)