Question

Find an equation of the circle that has center (-1, 3) and passes through (-4, -2)

Answer 1

Answer:

Your answer would be    $(x + 1)^{2} + (y - 3)^{2} = {34}$ .

Step-by-step explanation:

The formula for the equation of a circle is $(x - h)^{2} + (y - k)^{2} = r^{2}$, 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 $(x + 1)^{2} + (y - 3)^{2}$. 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  $d = \sqrt{34}$, so the radius is $\sqrt{34}$. But, we want the radius squared, which is 34. So, the final answer is what I wrote above.

Hope that helped! :)