Given an ellipse `(x^2)/(a^2)+ y^2/b^2=1 (a > b)` with foci at S and S' and vertices at A and A'. A tangent is drawn at any point P on the ellipse at and let R, R', B, B' respectively be the feet of the perpendiculars drawn from S. S', A. A' on the tangent at P. Then the ratio of the areas of the quadrilaterals S'R'RS and A'B' BA

Consider an ellipse x^2/25+y^2/9=1 with centre c and a point P on it with eccentric angle pi/4. Nomal drawn at P intersects the major and minor axes in A and B respectively. N_1 and N_2 are the feet of the perpendiculars from the foci S_1 and S_2 respectively on the tangent at P and N is the foot of the perpendicular from the centre of the ellipse on the normal at P. Tangent at P intersects the axis of x at T.

Equation of the ellipse is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci S_(1) and S_(2) The maximum area of the triangle P S_(1) S_(2) , where P is any point on the ellipse is

If P is any point lying on the ellipse x^2/a^2+y^2/b^2=1 , whose foci are S and S' . Let /_PSS'=alpha and /_PS'S=beta ,then

If P is any point lying on the ellipse x^2/a^2+y^2/b^2=1 , whose foci are S and S' . Let /_PSS'=alpha and /_PS'S=beta ,then

Let d and d^(') be the perpendicular distances from the foci of an ellipse to the tangent at P on the ellipse whose foci are S and S^(') . Then S^(')P:SP=

The product of the perpendiculars from the foci on any tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 is

If P (theta) is a point on the ellipse E (a gt b) , whose foci are S and S', then SP.S'P =