# Find the points of intersection of a line and a circle

#### penguin_alexa

##### New member
How do I algebraically prove how many times the line y=-5 intersects the circle (x-3)^2 + (y+2)^2 =25?

#### Cbarker1

##### Active member
What do you think you should do with y?

we get $(x-3)^2 + (-5+2)^2 = (x-3)^3+ 9 = 25$ or $(x-3)^2 = 16$