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.