If the tangent at `theta` on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` meets the auxiliary circle at two points which subtend a right angle at the centre then `e^(2)(2-cos^(2)theta)`=

The tangent at the point alpha on the ellipse x^2/a^2+y^2/b^2=1 meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity 'e' of the ellipse is given by the equation (A) e^2(1+cos^2alpha)=1 (B) e^2(cosec^2alpha-1)=1 (C) e^2(1+sin^2alpha)=1 (D) e^2(1+tan^2alpha)=1

The tangent at a point P(a cos phi,b sin phi) of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets its auxiliary circle at two points,the chord joining which subtends a right angle at the center.Find the eccentricity of the ellipse.

Equation auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a

The tangent at the point alpha on a standard ellipse meets the auxiliary circle in two points which subtends a right angle at the centre. Show that the eccentricity of the ellipse is (1+ sin^2aplha)^-1/2 .

the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

If omega is one of the angles between the normals to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the point whose eccentric angles are theta and (pi)/(2)+theta, then prove that (2cot omega)/(sin2 theta)=(e^(2))/(sqrt(1-epsilon^(2)))

[" If the tangent at the point "(h,k)" on "],[" the hyperbola "(x^(2))/(a^(2))-(y^(2))/(b^(2))=1" meets the "],[" auxiliary circle of the hyperbola "],[" in two points whose ordinates "],[y_(1),y_(2)" then "(1)/(y_(1))+(1)/(y_(2))=]

locus of the middle point of the chord which subtend theta angle at the centre of the circle S=x^(2)+y^(2)=a^(2)