SOLUTION: find the general form if the center is (-1,-4) and a point on the circle is (-1,1). show solution.

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Question 1005790: find the general form if the center is (-1,-4) and a point on the circle is (-1,1). show solution.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The size of the radius is 5, which you can find from y=-4 to y=1 using the given point on circle and the center point for the circle. (you could use the Distance Formula but that should not be needed here).

Standard Form %28x%2B1%29%5E2%2B%28y%2B4%29%5E2=25.

General Form: Multiply everything and simplify.
x%5E2%2B2x%2B1%2By%5E2%2B8y%2B16-25=0
x%5E2%2B2x%2By%5E2%2B8y%2B1%2B16-25=0
highlight%28x%5E2%2B2x%2By%5E2%2B8y-8=0%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


if the center is (h,k)=(-1,-4) and a point on the circle is (x,y)=(-1,1) we will use it to find the radius r
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
%28-1-%28-1%29%29%5E2%2B%281-%28-4%29%29%5E2=r%5E2
%28-1%2B1%29%5E2%2B%281%2B4%29%5E2=r%5E2
%280%29%5E2%2B%285%29%5E2=r%5E2
25=r%5E2
r=5

%28x%2B1%29%5E2%2B%28y%2B4%29%5E2=5%5E2
%28x%5E2%2B2x%2B1%29%2B%28y%5E2%2B8y%2B16%29=25
x%5E2%2B2x%2B1%2By%5E2%2B8y%2B16-25=0
x%5E2%2By%5E2%2B2x%2B8y%2B17-25=0
x%5E2%2By%5E2%2B2x%2B8y-8=0