Show that the length of the chord intercepted by the ellipse `x^2/a^2 + y^2/b^2 = 1` on the line `y= mx + c` is `2ab/(a^2 m^2 + b^2) sqrt((1+m^2) (a^2 m^2 + b^2 - c^2))`

The locus of mid point of tangent intercepted between area of ellipse x^2/a^2 +y^2/b^2 = 1 is

The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

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

The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Find the area of the smaller region bounded by the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and the line x/a+y/b=1

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

The minimum length of intercept of any tangent of ellipse x^2/a^2 + y^2/b^2 = 1 between axes is : (A) 2a (B) 2b (C) a+b (D) a-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 .

Locus of all such points from where the tangents drawn to the ellipse x^2/a^2 + y^2/b^2 = 1 are always inclined at 45^0 is: (A) (x^2 + y^2 - a^2 - b^2)^2 = (b^2 x^2 + a^2 y^2 - 1) (B) (x^2 + y^2 - a^2 - b^2)^2 = 4(b^2 x^2 + a^2 y^2 - 1) (C) (x^2 + y^2 - a^2 - b^2)^2 = 4(a^2 x^2 + b^2 y^2 - 1) (D) none of these

Prove that the ellipse x^2/a^2 + y^2/b^2 = 1 and the circle x^2 + y^2 = ab intersect at an angle tan^(-1) (|a-b|/sqrt(ab)) .