SOLUTION: Find the equation of a circle which passes through(2,-3)and(-4,5) and having the center on 4x+3y+1=0

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Question 1087551: Find the equation of a circle which passes through(2,-3)and(-4,5) and having the center on 4x+3y+1=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Plotting the points and line, you see that the two points go through the line.
Do the midpoint of the line segment joining the two points is the center of the circle.
The distance between the two points is the diameter.
To find the center,
x%5Bc%5D=%282-4%29%2F2=-1
y%5Bc%5D=%28-3%2B5%29%2F2=1
(-1,1)
Use the distance formula,
D%5E2=%285-%28-3%29%29%5E2%2B%28-4-2%29%5E2
D%5E2=64%2B36
D%5E2=100
For the equation of a circle, you need the square of the radius,
%282R%29%5E2=100
4R%5E2=100
R%5E2=25
So then,
highlight%28+%28x%2B1%29%5E2%2B%28y-1%29%5E2=25%29+
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