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

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

Let two foci of an ellipse be S_(1)(2,3) and s_(2)(2,7) and the foot of perpendicular drawn from S1 upon any tangent to the ellipse be (-1,1) . If e be the eccentricity of ellipse and R be the radius of director circle of auxiliary circle of ellipse, then find the value of (eR^(2))/(2)

The line 3x-4y=12 is a tangent to the ellipse with foci (-2,3) and (-1,0). Find the eccentricity of the ellipse.

The product of the perpendiculars drawn from the two foci of an ellipse to the tangent at any point of the ellipse is

Let the two foci of an ellipse be (-1,0) and (3,4) and the foot of perpendicular from the focus (3,4) upon a tangent to the ellipse be (4,6). The foot of perpendicular from the focus (-1,0) upon the same tangent to the ellipse is

Show that the locus of the foot of the perpendicular on a vaying tangent to an ellipse from either of its foci is a concentric circle