Question

Write the equation of the circle with center (3, 2) and (−6, −4) a point on the circle.

A) (x + 6)2 + (y + 4)2 = 13
B) (x + 3)2 + (y + 2)2 = 117
C) (x − 6)2 + (y − 4)2 = 13
D) (x − 3)2 + (y − 2)2 = 117

Answer 1

D

Explanation:

Took the test

Answer 2

D.
`(x-3)^2 + (y-2)^2 = 117`

Explanation:

To write the equation of a circle, use the formula
`(x-h)^2+(y-k)^2 = r^2` where the center of the circle is (h, k).

This means the equation is
`(x-3)^2 + (y-2)^2 = r^2`.

Find the radius r by finding the distance between (3,2) and (-6,-4) using the distance formula.

`d = √((-6-3)^2 + (-4-2)^2) =√((-9)^2 + (-6)^2) =√(81+36) =√(117)`

Since the radius is √117 and therefore
`r^2 = 117`.

The equation is
`(x-3)^2 + (y-2)^2 = 117`.