A circle with a center at (5,-2) also has the point (8,2) that lies on the circle. What is the equation of the circle?

Question

A circle with a center at (5,-2) also has the point (8,2) that lies on the circle. What is the equation of the circle?

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Amara 1 week 2021-10-12T08:19:30+00:00 1 Answer 0

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    2021-10-12T08:21:27+00:00

    Answer:

    Step-by-step explanation:

    You get the center just by reading the given point.

    (x – 5)^2 + (x + 2)^2 = r^2 Notice that the center switches signs.

    (8,2) is given so that you can figure out the radius.

    The radius uses the distance formula to get from (5,-2) to (8,2)

    x1 = 5

    x2 = 8

    y1 = -2

    y2 = 2

    ==================

    formula

    d^2 = (x1 – x2)^2 + (y1 – y2)^2

    solution

    d^2 = (5 – 8)^2 + (-2 – 2)^2

    d^2 = (-3)^2 + (-4)^2

    d^2 = 9 + 16

    d^2 = 25

    ==================

    Answer

    (x – 5)^2 + (y + 2)^2  =  25

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