Normal at `(x_1, y_1)` and `(acostheta, b sin theta)`

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

The normal to the curve x=a(1+cos theta), y=a sin theta " at " 'theta ' always passes through the fixed point

The normal to the curve x=a(cos theta + theta sin theta), y=a(sin theta - theta cos theta) at any theta is such that

Find the equation of the normal to the curve x=a cos theta and y=b sin theta at theta

If ((x)/(a) sin theta -(y)/(b) costheta )=1 and ((x)/(a)costheta +(y)/(b) sin theta)=1 , prove that ((x^(2))/(a^(2))+(y^(2))/(b^(2)))=2.

If DeltaABC having vertices A (acostheta_1, asintheta_1), B (acostheta_2, asintheta_2), and C (acostheta_3, asintheta_3) are equilateral triangle, then prove that cos theta_1 + costheta_2 + cos theta_3 = 0 and sintheta_1 + sintheta33