The Product Of The Perpendiculars From The Foci Upon Any Tangent To The Ellipse  is

If  touches the ellipse , then its eccentricity angle θ is equal to

If the polar with respect to the parabola y² = 4ax touches the ellipse , then the locus of its pole is  

The locus of mid-point of the portions of the tangents to the ellipse  included between the axes is the curve 

The area of the parallelogram formed by tangents at the extremities of two conjugate diameters of the ellipse  is equal to

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse  is 90⁰ then the eccentricity is

The tangent and the normal to the ellipse x² + 4y² = 4 at a point P on it meet the major axis in Q and R respectively. If QR = 2, then the eccentric angle of P is

If CP and CD is a pair of semi-conjugate diameters of the ellipse,

, then CP² + CD² =

The line y = 2t² meets the ellipse  in real point if

The locus of the foot of the perpendiculars to any tangent of an ellipse from the foci is

If P and D are the extremities of a pair of conjugate diameters of the ellipse , then the locus of the middle point ofPD is