Show that the tangent to the ellipse `x^2/a^2+y^2/b^2=1` at points whose eccentric angles differ by `pi/2` intersect on the ellipse `x^2/a^2+y^2/b^2=2`

The equation of the normal to the ellipse x^(2)//16+y^(2)//9=1 at the point whose eccentric angle theta=pi//6 is

The equation of the normal to the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at the point whose eccentric angle is (pi)/(4) is

The points on the ellipse 2x^(2)+3y^(2)=6 whose eccentric angles differ by two right angles is

The eccentric angles of the extremities of latusrecta of the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 is

P(theta) and D(pi/2+theta) are two points on the ellipse x^2/a^2+y^2/b^2=1 . Show that the locus of the point of intersection of tangents at P and Q to the ellipse is x^2/a^2+y^2/b^2=2

The eccentric angles of the ends of L.R. of the ellipse (x^(2)/(a^(2))) + (y^(2)/(b^(2))) = 1 is

The area of the parallelogram formed by the tangents at the points whose eccentric angles are theta, theta + pi/2, theta + pi, theta +(3pi)/2 on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

The distance of a point on the ellipse x^(2)//6+y^(2)//2=1 from the centre is 2. The eccentric angle of the point is

Find the equations of tangent and normal to the ellipse 2x^2+3y^2=11 at the point whose ordinate is 1.

The slope of a common tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 and a concentric circle of radius r is