The Eccentricity Of An Ellipse With Centre At The Origin And Axes Along The Coordinate Axes, Is 1/2. If One Of The Directrices Is x = 4, Then The Equation Of The Ellipse Is  

The locus of the foot of the perpendicular from the foci on any tangent to the ellipse 

The locus of the point of intersection of tangents to the ellipse  at the points whose eccentric angles differ by  is  

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is 

The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is 

, be the end points of the latusrectum of the ellipse x² + 4y² = 4. The equations of parabolas with latusrectum PQ are 

The locus of the point of intersection of perpendicular tangents to.

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

The tangent at a point P(θ) to the ellipse  cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is

Let d₁ and d₂ be the lengths of the perpendiculars drawn from fociS and S’ of the ellipse  to the tangent at any point P on the ellipse. Then, SP : SP’ = 

If the tangents are drawn to the ellipse x² + 2y² = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is