NOTE: This system represents a **parabola** intersecting a
**circle***.* We expect:

- no intersection point or possibly
- 1, 2, 3 or 4 intersection points

If we subtract the first line from the second, we have:

y^{2}−y= 25 − 5

y^{2}−y− 20 = 0(

y+ 4)(y− 5) = 0So

y= −4 or 5

The corresponding *x* values are going to be:

`x = +3` or ` −3`, and `x = 0`

So the solution set will be:

`(−3,−4)`, `(3,−4)` and `(0,5)`.

The sketch shows:

Graphs of `y = -x^2+5` and `x^2+y^2=25`: Intersection parabola and circle

We can see from the graph that our 3 solutions `(−3,−4)`, `(3,−4)` and `(0, 5)` are correct.

Get the Daily Math Tweet!

IntMath on Twitter