Find the equation of a circle with a center at (0, -4) and a point on the circle is (6, 0).

Question

Find the equation of a circle with a center at (0, -4) and a point on the circle is (6, 0).

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RuslanHeatt 4 years 2021-08-08T11:51:41+00:00 1 Answers 16 views 0

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  1. Verity
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    2021-08-08T11:53:14+00:00
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    Answer:

    x^2 + ( y + 4)^2 = 52

    Step-by-step explanation:

    Equation of circle with center (a , b) and radius, r is :

    (x -a)^2 + ( y -b)^2 = r^2

    Given :  a = 0 , b = – 4

    Step 1 : Find the radius.

           Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , – 4) of the circle and ( 6 , 0 ) gives the radius of the circle.

       r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\

         = \sqrt{ 36 + 16 } \\\\= \sqrt{52}

    Step 2 : Equation of circle.

      (x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52

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