Locus of foot of perpendicular from focus upon any tangent is tangent at vertex OR Image of focus in any tangent lies in Directrix

Prove that perpendicular drawn from focus upon any tangent of a parabola lies on the tangent at the vertex

The locus of foot of the perpendiculars drawn from the focus on a variable tangent to the parabola y^2 = 4ax is

The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as (-3, -2) and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The directrix of the hyperbola corresponding to the focus (5, 6) is

The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as (-3, -2) and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The point of contact of the tangent with the hyperbola is

The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as (-3, -2) and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The conjugate axis of the hyperbola is

Let F be the focus of the parabola y^(2)=4ax and M be the foot of perpendicular form point P(at^(2), 2at) on the tangent at the vertex. If N is a point on the tangent at P, then (MN)/(FN)"equals"

Prove that the locus of the foot of the perpendicular drawn from the focus of the parabola y ^(2) = 4 ax upon any tangent to its is the tangent at the vertex.

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

If the locus of the middle of point of contact of tangent drawn to the parabola y^2=8x and the foot of perpendicular drawn from its focus to the tangents is a conic, then the length of latus rectum of this conic is 9/4 (b) 9 (c) 18 (d) 9/2

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