### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem9-152

9-152.

Sketch both the circle $x^{2} + y^{2} = 25$ and the parabola $y = x^{2} − 13$.

1. How many points of intersection are there?

Look at the graph at right.

$4$ points

2. Find the coordinates of these points algebraically.

Substitute $x^{2} − 13$ into the first equation.

x$^{2} + \left(x^{2} − 13\right)^{2} = 25$

Solve for $x$.

$x^{4} − 25x^{2} + 144 = 0$

Factor the equation.

$\left(x^{2} − 16\right)\left(x^{2} − 9\right)$

$\left(x − 4\right)\left(x + 4\right)\left(x − 3\right)\left(x + 3\right)$

$x = ±4, ±3$

Now substitute in these $x$ values to find the $y.$