1. The general equation of a parabola is

where p is the distance between the vertex and the focus.

2. The vertex has in your case the coordinates V(0, 0). Let

a point on the given parabola. The the midpoint of the chord

is

.

3. All points M form a curve. You know that the x-value is:

You know that the y-value is:

Plug in the term for k:

4. The equation of the new parabola is:

Now determine the vertex and the focus of the new parabola and compare them with the corresponding values of the given parabola.