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

If p and p’ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respectively, on a tangent to the ellipse and r denotes the focal distance of the point, then     

If circumcentre of an equilateral triangle inscribed in  with vertices having eccentric angle α, β, γ respectively is (x₁, y₁) then 

Locus of the middle points of all chords of , which are at a distance of 2 units from the vertex of parabola y² = –8axis

A point on the ellipse  at a distance equal to the mean of lengths of the semi-major and semi-minor axis from the centre, is

A tangent to the ellipse  is cut by the tangent at the extremities of the major axis at T and T’. The circle on TT’ as diameter passes through the point

If C is the centre and A, B are two points on the conic

4x² + 9y² – 8x – 36y + 4 = 0 such that ∠ACB = π/2 then CA^–2 +CB^–2 is equal to  

Ellipses which are drawn with the same two perpendicular lines as axes and with the sum of the reciprocals of squares of the lengths of their semi-major axis and semi-minor axis equal to a constant have only.

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 

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