Area of the triangle formed by the tangents at the point on the ellipse `x^2/a^2+y^2/b^2=1` whose eccentric angles are `alpha,beta,gamma` is

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

The area of the triangle formed by the tangent at the point (a, b) to the circle x^(2)+y^(2)=r^(2) and the coordinate axes, 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 minimum area of the triangle formed by the tangent to the ellipse (x^(2))/(16) + (y^(2))/(9) =1 and the co-ordinate axes is

The area of the triangle formed by any tangent to the hyperbola x^(2) //a^(2) -y^(2) //b^(2) =1 with its asymptotes is

Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points whose eccentric angles are alpha-beta and alpha+beta The coordinates of their point of intersection are

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

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

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

The eccentric angles of the vertices of a triangle inscribed in the ellipse x^2/a^2 + y^2/b^2 =1 are alpha, beta, gamma , then for the area of this triangle to be greatest, the angle subtended by the two consecutive vertices of the triangle at the centre of the ellipse in degree measure is...