Chords of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.

Find the locus of the middle points of chord of an ellipse x^2/a^2 + y^2/b^2 = 1 which are drawn through the positive end of the minor axis.

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

If two points are taken on the minor axis of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a^2dot

The locus of the midpoints of the chords of an ellipse x^(2) + 4y^(2) = 4 that are drawn forms the positive end of the minor axis is

A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which has O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.

Show tht the locus of the middle points of chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 drawn through an extremity of the minor axis is (x^(2))/(a^(2))+(y^(2))/(b^(2)) = pm (y)/(b)

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with A A ' as the major axis. Find the maximum area of triangle A P A '

Find the locus of the middle points of chords of an ellipse drawn through the positive extremity of the minor axis