The locus of the feet of the perpendicular to any tangent of an ellipse from the foci is

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

If the loucus of the feet of perpendicular from the foci on any tangent to an ellipse (x^(2))/(4) + (y^(2))/(2) =1 is x^(2) + y^(2) =k , then the value of k is _______.

the foot of perpendicular from a focus on any tangent to the ellipse x^2/4^2 + y^2/3^2 = 1 lies on the circle x^2 + y^2 = 25 . Statement 2: The locus of foot of perpendicular from focus to any tangent to an ellipse is its auxiliary circle.

The sum of the squares of the perpendiculars on any tangent to the ellipse a 2 x 2 ​ + b 2 y 2 ​ =1 from two points on the minor axis, each at a distances ae from the centre, is

Show that the locus of the foot of the perpendicular drawn from centre on any tangent to the ellipse b^2x^2+a^2y^2=a^2b^2 is the curve (x^2+y^2)^2=a^2x^2+b^2y^2

The locus of the foot of the perpendicular from the centre of the ellipse x^2 +3y^2 =3 on any tangent to it is

Let S=(3,4) and S'=(9,12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent of the ellipse is (1, -4) then the eccentricity of the ellipse is

If the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse (x^(2))/(40)+(y^(2))/(10)=1 is (x^(2)+y^(2))^(2)=ax^(2)+by^(2) , then (a-b) is equal to

The locus of the point of intersection of the perpendicular tangents to the ellipse 2x^(2)+3y^(2)=6 is

The sum fo the squares of the perpendicular on any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from two points on the mirror axis, each at a distance sqrt(a^(2) - b^(2)) from the centre, is