Given that where and , prove that:

a) ifuvaries butvis constant, then the locus of is a parabola,

b) ifvvaries anduis constant, then the locus of P is again a parabola.

Show that these two parabolas have the same axis and focus.

From the relation:

Which is the parametric equation for a parabola.

Whenuvaries, the parabola has focus and axis .

Whenvvaries, the parabola has focus and axis .

The parabolas face in opposite directions, and both cross the y-axis, assuming that the constants are greater than 0. My problem is how do I show that they have the same focus. They do have the same axis.

Thanks!