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. 


We are given the center of the circle at (a,b)=(-3,-4), so our equation becomes



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.



This is the equation for our circle in standard form. The equation for a circle in general form looks like


To translate our equation to general form. Multiply everything out.


Subtract 36 from both sides and combine like terms. Then rearrange in the proper order.


The equation in general form is

 
Feel free to email me if your have questions about the solution.

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