If SY and S'Y' be drawn perpendiculars from foci to any tangent to a hyperbola. Prove that y and Y' lie on the auxiliary circle and that product of these perpendicular is constant.

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

Prove that the tangents to the circle x^(2)+y^(2)=25 at (3,4) and (4,-3) are perpendicular to each other.

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be x^2+y^2=6 (b) x^2+y^2=9 x^2+y^2=3 (d) x^2+y^2=18

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Find the length of the perpendicular drawn from the point (2, 3, 7) to the plane 3x - y - z = 7. Also find the coordinates of the foot of the perpendicular.

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

Two perpendicular tangents to the circle x^2 + y^2= a^2 meet at P. Then the locus of P has the equation

Find the foot of perpendicular drawn from origin to the plane 2x+3y+4z-12=0

If p be the length of the perpendicular from the origin on the line x/a+y/b=1 , then