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Find the points of intersection of a line and a circle

penguin_alexa

New member
May 8, 2020
1
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
Jan 8, 2013
227
MN
What do you think you should do with y?
 

kaliprasad

Well-known member
Mar 31, 2013
1,261
Bangalore india
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)