SOLUTION: What is the equation of a circle in general form whose center is at (-3,-4) and passes through the point (1,2)

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Question 858395: What is the equation of a circle in general form whose center is at (-3,-4) and passes through the point (1,2)

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,

Problem:
What is the equation of a circle in general form whose center is at (-3,-4) and passes through the point (1,2)?

Solution:
Begin with the equation for a circle in standard form where (a,b) is the center of the circle and r is its radius. 
%28x-a%29%5E2+%2B+%28y-b%29%5E2=r%5E2

We are given the center of the circle at (a,b)=(-3,-4), so our equation becomes
%28x-%28-3%29%29%5E2+%2B+%28y-%28-4%29%29%5E2+=+r%5E2
%28x%2B3%29%5E2+%2B+%28y%2B4%29%5E2+=+r%5E2

We all have a point (1,2) on the circle. Substitute 1 for x and 2 for y into the circle to find the radius r^2.
%281%2B3%29%5E2+%2B+%282%2B4%29%5E2+=+r%5E2


This is the equation for our circle in standard form. The equation for a circle in general form looks like
x%5E2%2By%5E2%2BAx%2BBy%2BC%2B0

To translate our equation to general form. Multiply everything out.
x%5E2%2B6x%2B9%2By%5E2%2B8y%2B16=52

Subtract 36 from both sides and combine like terms. Then rearrange in the proper order.
x%5E2%2B6x%2By%5E2%2B8y-27=0

The equation in general form is
x%5E2%2By%5E2%2B6x%2B8y-27=0
 
Feel free to email me if your have questions about the solution.

~Mrs. Figgy
math.in.the.vortex@gmail.com