## Circle and parabola

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
mitnord
Posts: 13
Joined: Mon Feb 23, 2009 11:17 pm
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### Circle and parabola

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
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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!