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 line x = at² meets the ellipse  in the real points iff

On the ellipse 4x² + 9y² = 1, the points at which the tangents are parallel to the line 8x = 9y are

Tangent is drawn to the ellipse  , then the value of θ such that sum of intercepts on axes made by the tangent is minimum 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  

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