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.

If the normal at an end of a latus-rectum of an elipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through one extremity of the minor axis,show that the eccentricity of the ellipse is given by e^(4)+e^(-1)=0

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

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.

S and T 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 STB is an equilateral triangle,the eccentricity of the ellipse is e then find value of 4e