[" (1) "a^(2)quad b^(2)],[" (j) "4x^(2)+9y^(2)=36" Points of "(3cos theta,2sin theta)" On. "]

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 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 cot beta)/(sin 2 theta) is equal to:

tangents are drawn to x^(2)+y^(2)=a^(2) at the points A(a cos theta,a sin theta) and B(a cos(theta+(pi)/(3)),a sin(theta+(pi)/(3))) Locus of intersection of these tangents is

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0

Find (dy)/(dx) if x= 3 cos theta - cos 2theta and y= sin theta - sin 2theta.

Find (dy)/(dx) if x= 3 cos theta - cos 2theta and y= sin theta - sin 2theta.

cos (2 theta) cos ((theta) / (2)) - cos (3 theta) cos ((9 theta) / (2)) = sin (5 theta) sin ((5 theta) / (2))