How do you write an equation for a circle given center (4,2) and tangent to the x-axis?

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Answer 1 · 2016-10-30T06:29:27

Please see the explanation.

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x - h)^2 + (y - k)^2 = r^2$

where $(h, k)$ $(h,k)$ is the center point and r is the radius

Substitute the center point $(4, 2)$ $(4, 2)$ into the standard form:

${(x - 4)}^{2} + {(y - 2)}^{2} = r^{2}$ $(x - 4)^2 + (y - 2)^2 = r^2$

Because the center is 2 units above the x axis and the circle is tangent to the x axis, the radius must be 2:

${(x - 4)}^{2} + {(y - 2)}^{2} = 2^{2}$ $(x - 4)^2 + (y - 2)^2 = 2^2$