The Equation Of The Ellipse With Focus (–1, 1), Directrix x – Y + 3 = 0 And Eccentricity , Is

The product of the perpendiculars from the foci upon any tangent to the ellipse  is

If P and D are the extremities of a pair of conjugate diameters of the ellipse , then the locus of the middle point ofPD is

The equation of the ellipse, referred to its axes as the axes of coordinates, which passes through the points (2, 2) and (1, 4) is

If CP and CD be any two semi-conjugate diameters of the ellipse  and the circle with CP and CD as diameters intersect in R, then R lies on the curve

The locus of the point whose polar with respect to the ellipse  touches the parabola y² = 4kx is 

The polar of lx + my =1 with respect to the ellipse  lies on the ellipse  if

The locus of the poles of the tangents to the ellipse  w.r.t. the circle x² + y² = a² is

A variable point P on the ellipse eccentricity e is joined to its foci S, S’. The locus of the incentre of   is an ellipse of eccentricity

The locus of the point of intersection of two perpendicular tangent to the ellipse , is

The equation of the ellipse whose center is at origin and whihch passes through the points (–3, 1) and (2, –2) is