If F1 and F2 be The Feet Of The Perpendicular From The Foci S1and S2 of An Ellipse  on The Tangent At Any Point P on The Ellipse, Then (S1F1)(S2F2) Is Equal To   

, then PF₁ + PF₂ equals

An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an

The sum of the squares of the perpendicular on any tangent to the ellipse  from two points on the minor axis, each at a distance  from the centre is 

The eccentric angle of a point on the ellipse  whose distance from the centre of the ellipse is 2, is

If any tangent to the ellipse  intercepts equal length lon the axes, then l =

The ellipse x² + 4y² = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is  

A focus of an ellipse is at the origin. The directrix is the line  x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis, is  

In an ellipse, the distance between its foci is 6 and minor axis is 8. The eccentricity is 

The tangent at a point  meets the auxiliany circle in two points. The chord joining them subtends a right angle at the centre. Then, the eccentricity of the ellipse is given by  

The area of the rectangle formed by the perpendiculars from the centre of the ellipse to the tangent and normal at the point-whose eccentric angle is , is