The coordinates of the foot of the perpendicular drawn from the origin upon a line are (h,k) , show that the equation of the line is `hx+ky=h^(2)+k^(2)(h^(2)+k^(2)ne0)`.

The co-ordinates of the foot of the perpendicular drawn fromthe origin upon a line are (h,k); show that the equation of the line is hx+ky=h^(2)+k^(2),(h^(2)+k^(2)0)

The co-ordinates of the foot of perpendicular drawn from origin to a line are (2,3) . Find the equation of the line.

Find the locus of the foot of the perpendicular from the origin to the line which always passes through a fixed point(h, k).

If Q(h,k) is the foot of the perpendicular from P(x_(1) ,y_(1)) on the line ax + by+ c=0 then Q(h,k) is

A point moves so that the distance between the foot of perpendiculars from it on the lines a x^2+2hx y+b y^2=0 is a constant 2d . Show that the equation to its locus is (x^2+y^2)(h^2-a b)=d^2{(a-b)^2+4h^2}dot

A point moves so that the distance between the foot of perpendiculars from it on the lines a x^2+2hx y+b y^2=0 is a constant 2d . Show that the equation to its locus is (x^2+y^2)(h^2-a b)=d^2{(a-b)^2+4h^2}dot

A point moves so that the distance between the foot of perpendiculars from it on the lines a x^2+2hx y+b y^2=0 is a constant 2d . Show that the equation to its locus is (x^2+y^2)(h^2-a b)=d^2{(a-b)^2+4h^2}dot

P( h, k) is the mid-point of a line segment between axes. Show that equation of the line is x/a + y/b = 2 .

A straight line passes through (h, k) and the middle point of the also (h, k). Show that the equation of straight line kx + hy = 2hk.