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

The slope of a common tangent to the ellipse  and aconcentric circle of radius r is

P is a variable point on the ellipse  with AA’ as the major axis. Then, the maximum value of the area of the triangleAPA’ is   

The equation of the ellipse whose distance between the foci is equal to 8 and distance between the directrices is 18, is

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 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