SOLUTION: The circle x^2+y^2+2x-4y-11=0 and the line x-y+1=0 intersect at A and B. Find the equation of the circle having AB as diameter.

Algebra ->  Circles -> SOLUTION: The circle x^2+y^2+2x-4y-11=0 and the line x-y+1=0 intersect at A and B. Find the equation of the circle having AB as diameter.      Log On


   

Question 1020926: The circle x^2+y^2+2x-4y-11=0 and the line x-y+1=0 intersect at A and B. Find the equation of the circle having AB as diameter.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Find the intersection points.
Find midpoint of these.
Find distance from that midpoint to either of the intersection points; this will be the radius.
Fit into the standard equation form of a circle.

x=y-1
-
%28y-1%29%5E2%2By%5E2%2B2%28y-1%29-4y-11=0
y%5E2-2y%2B1%2By%5E2%2B2y-2-4y-11=0
2y%5E2-12=0
y%5E2-6=0
y=0%2B-+sqrt%286%29
-
x=-1-sqrt%286%29 or x=-1%2Bsqrt%286%29
meaning the intersections are at (-1-sqrt(6),-sqrt(6)) and (-1+sqrt(6),sqrt(6)).

Midpoint of those points:
x=-2%2F2=-1 and y=0.
This means, the center of the asked-for circle will be (-1,0).

RADIUS will be r=sqrt%28%28-1-%28-1%2Bsqrt%286%29%29%29%5E2%2B%280-sqrt%286%29%29%5E2%29
r=sqrt%286%2B6%29
r=sqrt%2812%29

Put the information into standard form equation of a circle to finish the asked-for circle:
highlight%28%28x%2B1%29%5E2%2By%5E2=12%29
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