Question

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?

Answer 1

Please see the explanation.

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.