The Equation Of The Ellipse With Its Centre At (1, 2), One Focus At (6, 2) And Passing Through (4, 6) Is

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 

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 

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