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 `(2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))`

Find the equation of the normal to the hyperbola 4x^(2) - 9y^(2) = 144 at the point whose eccentric angle theta is pi//3

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

If theta is the angle between the asymptotes of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 with eccentricity e , then sec (theta/2) can be

The line (x)/(a)cos theta-(y)/(b)sin theta=1 will touch the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at point P whose eccentric angle is (A) theta(B)pi-theta(C)pi+theta(D)2 pi-theta

If beta is one of the angles between the normals to the ellipse, x^2+3y^2=9 at the points (3 cos theta, sqrt(3) sin theta)" and "(-3 sin theta, sqrt(3) cos theta), theta in (0,(pi)/(2)) , then (2 cos beta)/(sin 2 theta) is equal to:

If (x)/(a)+(y)/(b)=sqrt(2) touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then find the eccentric angle theta of point of contact.

The points P,Q,R are taken on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentric angles theta,theta+a,theta+2a, then area of ,Delta PQR is independent of

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) =

If x=a sin theta and y=b tan theta, then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is