Let the line `2y=_x+k` is tangent to the ellipse` x^2/a^2+y^2/11=1 (a^2>11)` which cuts its auxiliary circle at points A and B such that `/_AOB=90^@` If e is the eccentricity of ellipse, then value of `8e^2` is (O is origin)

If e be the eccentricity of ellipse 3x2+2xy+3y^(2)=1 then 8e^(2) is

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

The auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

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 to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point R and Q , then find the points of intersection of tangents to the circle at Q and Rdot

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) =