Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1.`

The locus of the foot of perpendicular from the forcus on any tangent to y^(2) = 4ax is

the locus of the foot of perpendicular drawn from the centre of the ellipse x^2+3y^2=6 on any point:

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

Find the foot of the perpendicular from the point (2,4) upon x+y=1.

If two points are taken on the minor axis of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a^2dot

Locus of perpendicular from center upon normal to the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 is

Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola 16y^2 -9 x^2 = 1 is

Statement 1 : For the ellipse (x^2)/5+(y^2)/3=1 , the product of the perpendiculars drawn from the foci on any tangent is 3. Statement 2 : For the ellipse (x^2)/5+(y^2)/3=1 , the foot of the perpendiculars drawn from the foci on any tangent lies on the circle x^2+y^2=5 which is an auxiliary circle of the ellipse.

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= (a) d_1: d_2 (b) d_2: d_1 (c) d_1 ^2:d_2 ^2 (d) sqrt(d_1):sqrt(d_2)

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (x^2-y^2)=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)