Let S and S’ Be Two Foci Of The Ellipse . If A Circle Described On SS’ As Diameter Intersects The Ellipse In Real And Distinct Points, Then The Eccentricity e of The Ellipse Satisfies   

The eccentricity of the ellipse with centre at the origin which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lie along the axes of  coordinates is

The radius of the circle passing through the foci of the ellipse

9x² + 16y² = 144 and having its centre at (0, 3), is 

An ellipse has OB as a semi-minor axis, F, F’ as its foci and the angle ∠FBF’ is a right angle. Then, the eccentricity of the ellipse is

The focus of an ellipse is (–1, –1) and the corresponding directix is x – y + 3 = 0. If the eccentricity of the ellipse is 1/2, then the coordinates of the centre of the ellipse are 

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through (4, 6) is

Tangents are drawn to the ellipse  and the circle x² + y² = a² at the points where a common ordinate cuts them (on the same side of the x-axis). Then, the greatest acute angle between these tangents is given by 

The area of the quadrilateral formed by the tangents at the end-points of latusrecta to the ellipse 

If α – β = constant, then the locus of the point of intersection of tangents at  to the ellipse   

Let S(3, 4) and S’(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent to the ellipse is (1, –4), then the eccentricity of the ellipse is 

If PSQ is a focal chord of the ellipse , then the harmonic mean of SP and SQ is