How do you write an equation of a circle with d=12 and center translated 18 units left and 7 units down from the origin?

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Answer 1 · 2016-12-15T19:01:17

Please see the explanation.

The standard form for the equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2" [1]"$

where $(x, y)$ is any point on the circle, $(h, k)$ is the center, and r is the radius.

The diameter is 12, therefore, the radius is 6. Substitute 6 for r into equation [1]:

$(x - h)^2 + (y - k)^2 = 6^2" [2]"$

The center is moved $(-18, -7)$ , therefore, substitute -18 for h and -7 for k into equation [2]:

$(x - -18)^2 + (y - -7)^2 = 6^2" [3]"$

Equation [3] is the answer.

You may be tempted to write this as:

$(x + 18)^2 + (y + 7)^2 = 36$

but I do not recommend it, because it makes it harder to observe the center and the radius.