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

9-152.

Sketch both the circle

*x*^{2}+*y*^{2}= 25 and the parabola*y*=*x*^{2}− 13. Homework Help ✎How many points of intersection are there?

Find the coordinates of these points algebraically.

Look at the graph at right.

4 points

Substitute *x*^{2} − 13 into the first equation.*x*^{2} + (*x*^{2} − 13)^{2} = 25

Solve for *x*.*x*^{4} − 25*x*^{2} + 144 = 0

Factor the equation.

(*x*^{2} − 16)(*x*^{2} − 9)

(*x* − 4)(*x* + 4)(*x* − 3)(*x* + 3)

*x* = ±4, ±3

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