If Any Tangent To The Ellipse  intercepts Equal Length lon The Axes, Then l =

A straight line PQ touches the ellipse  and the circle x² + y² = r² (b < r < a). RS is a focal chord of the ellipse. If RSis parallel to PQ and meets the circle at points R and S. Find the length of RS. 

If α and β are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is 

, then the chord joining two points θ₁ and θ₂ on the ellipse  will subtend a right angle at

The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is a/an

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

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