Posted by **mani** on Tuesday, April 2, 2013 at 12:42pm.

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

- geometry -
**Steve**, Tuesday, April 2, 2013 at 1:35pm
we can without loss of generality let the line be the x-axis, 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 + (k-y)^2)

y^2 = x^2 + y^2 - 2ky + k^2

2ky = x^2+k^2

it's still a parabola.

## Answer this Question

## Related Questions

- geometry - A point is moving in a plane in such a way that its distance from the...
- Geometry - Okay heres the pic. There is a plane with points B,D, and E.those [...
- Geometry - 4.Determine which point does not lie on the graph of the line y=x-3 a...
- Math - Okay heres the pic. There is a plane with points B,D, and E.those [oints...
- Geo Hons - Okay heres the pic. There is a plane with points B,D, and E.those [...
- geometry - A small airplane takes off from point A and continues to climb upward...
- Physics - The drawing shows four point charges. The value of q is 2.4 µC, and ...
- Precalc - At the point were a line intersects a plane [with the equation (24x+...
- trigonometry - The angle of elevation of the top of a tower to point A on the ...
- Physics repost - Posted by Mary on Monday, September 3, 2007 at 7:11pm. download...