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  

, 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

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  

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