The tangent at a point `P(acosvarphi,bsinvarphi)` 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.

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.

The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:

The tangent at the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , meets its auxiliary circle at two points whose join subtends a right angle at the centre, show that the eccentricity of the ellipse is given by, (1)/(e^(2))=1+sin^(2)theta

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 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

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 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 .

If the chord joining the points (2,-1),(1,-2) subtends a right angle at the centre of the circle,then its centre and radius are