Find the points of intersection of a line and a circle

[penguin_alexa]

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

 

[cbarker1]

What do you think you should do with y?

 

[kaliprasad]

you can put y = -5 to solve for x

we get $(x-3)^2 + (-5+2)^2 = (x-3)^3+ 9 = 25$ or $(x-3)^2 = 16$
now you can solve to get x = 3 + 4 = 7 or 3-4 = - 1 so it intersects at 2 points (7,-5) and (-1,-5)