Answer:
Your answer would be [tex](x + 1)^{2} + (y - 3)^{2} = {34}[/tex] .
Step-by-step explanation:
The formula for the equation of a circle is [tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex], where (h, k) is the center of the circle, and r is the radius. Since the center is (-1, 3), the left half of the equation is [tex](x + 1)^{2} + (y - 3)^{2}[/tex]. Now, all we have to do now is find the radius, r. To do that, you can use the distance formula to find the distance between the center (-1, 3) and a point that passes through the circle, or is on the circumference, (-4, -2). When you calculate that, you will get [tex]d = \sqrt{34}[/tex], so the radius is [tex]\sqrt{34}[/tex]. But, we want the radius squared, which is 34. So, the final answer is what I wrote above.
Hope that helped! :)
