# How do you solve x^2 + y^2 = 9 and x^2 – 3y = 9?

Sep 4, 2015

Solution is (-3,0), (3,0) and (0,-3)

#### Explanation:

${x}^{2} + {y}^{2} = 9$ represents a circle centered at (0,0) with radius 3 and ${x}^{2} - 3 y = 9$ represents a vertical parabola opening up with its vertex at (0,-3). These intersect at 3 points which can be determined graphically or algebraically.

Solving algebraically, it would be $3 y + 9 + {y}^{2} = 9$, which means y(y+3)=0. Thus y=0, -3

For y=0, the equation of circle gives x= 3, -3, hence two of the points are (-3,0) and (3,0)

For y=-3, the circle equation gives x=0, hence the third point is (0,-3)