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

Question

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

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Katherine 2 weeks 2021-09-10T15:45:10+00:00 1 Answer 0

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    2021-09-10T15:46:24+00:00

    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! 🙂

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