Write the standard equation of a circle that passes through (−4, 0) with center (−1, −4).

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Write the standard equation of a circle that passes through (−4, 0) with center (−1, −4).

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    0
    2021-11-26T09:25:35+00:00

    Modify the std eqn of a circle with center at (h,k) to find the radius r:

    (-4+1)^2 + (0+4)^2 = r^2.  Then 9 + 16 = 25, and so r^2 = 25, and r = +5.

    The equation is (x+1)^2 + (y+4)^2 = 25.

    0
    2021-11-26T09:26:13+00:00

    the equation of a circle is defined by:  (x - h)^{2} +  (y - k)^{2} =  r^{2} where (h,k) is the center of the circle and “r” is the radius. So we need to find the radius, which is the distance between the center (-1,-4) and the point on the circle (-4, 0). Do this using the distance formula: d =  \sqrt{( x_{2 -} x_{1})^2 + ( y_{2}-  y_{1})^2    }

    so distance =  \sqrt{(-4 - 0)^2 + (-1 + 4)^2} =  \sqrt{25} = 5
    Now we just write the equation:  (x +1)^2 + (y + 4)^2 = 25

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