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 number of values of c such that the straight line y = 4x + ctouches the curve , is  

, 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 

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