geometry
posted by mani on .
a point F is at a certain distance from a line AB .Another point P is moving in a plane such that the ratio of it's distance from F and line AB remains constant .find the locus of the point P

we can without loss of generality let the line be the xaxis, and F be at (0,k+1).
We know that if the ratio is 1, the locus is a parabola. Maybe it still is.
If P starts at (0,1) the ratio is k. We have
y = √(x^2 + (ky)^2)
y^2 = x^2 + y^2  2ky + k^2
2ky = x^2+k^2
it's still a parabola.