Write the equation of the circle whose center is (-4,8) and has a diameter of 18

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Write the equation of the circle whose center is (-4,8) and has a diameter of 18

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Gerda 3 years 2021-09-04T08:57:39+00:00 1 Answers 5 views 0

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  1. Dulcie
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    2021-09-04T08:58:41+00:00
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    Answer:

    (x + 4)^2 + (y – 8)^2 = 81

    or

    (x + 4)^2 + (y – 8)^2 = 9^2 depending on how your teacher wants it written.

    Step-by-step explanation:

    The standard form for a circle is

    (x + h)^2 + (y + k)^2 = r^2

    r is the radius.

    You are given the diameter

    r = d/2

    r = 18/2

    r = 9

    So you already have the right hand side of the equation

    (x + h)^2 + (y + k)^2 = 9*2

    (x + h)^2 + (y + k)^2 = 81

    You basically have h and k as well. They come from the center point.

    h = 4

    k = – 8

    So the equation of the circle (and the answer) is

    (x + 4)^2 + (y – 8)^2 = 81

    One question remains. Why do the x and y values change signs? If you know what the distance formula is, then what you are finding is the distance r of all points on the circle from the center of the circle.

    It is the distance formula that is actually the formula for the circle.

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