Circle and parabola

[mitnord]

Hi,

A circle is given as (x - 3)^2 + (y + 4)^2 = 25 with
C(3, -4)
r = 5

A parabola is given as y = x^2 + 2x + a

For which values of 'a' the vertex of the parabola lies on the circle?

Any help appreciated.
Thanks!

[stapel_eliz]

A circle is given as (x - 3)^2 + (y + 4)^2 = 25 with C(3, -4) r = 5

A parabola is given as y = x^2 + 2x + a

For which values of 'a' the vertex of the parabola lies on the circle?

First, find the x-coordinate of the vertex of the parabola, either by completing the square or by using a formula. This part does not depend on the value of "a".

Then, plug this x-value into each of the two equations. This will give you a system of non-linear equations that you can solve for "y" and "a" (or just for "a", if you prefer).

If you get stuck, please reply showing your steps and reasoning. Thank you!