Which of the following equations of a circle has center at (1, -3) and radius of 5?

x^{2} + y^{2} = 25

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{(x - 1)}^{2} + {(y + 3)}^{2} = 25

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{(x - 1)}^{2} + {(y - 3)}^{2} = 25

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{(x + 1)}^{2} + {(y - 3)}^{2} = 25

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Solution

The correct option is D ${(x - 1)}^{2} + {(y + 3)}^{2} = 25$
the general equation of a circle with center at (a,b) and radius r is
$(x - a)^{2} + (y - b)^{2} = r^{2}$
so substituting the values we get the circle equation as
$(x - 1)^{2} + (y + 3)^{2} = 25$ option B

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