### Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-151

8-151.

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.

$4$ points

2. Find the coordinates of these points algebraically.

Substitute $x^² - 13$ into the first equation.  $x^2 + (x^2 - 13)^2 = 25$

Solve for $x$.  $x^4 - 25x^2 + 144 = 0$

Factor the equation.  $(x^² - 16)(x^² - 9)$

$(x − 4)(x + 4)(x − 3)(x + 3)$

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

$x = \pm4, \pm3$