Question

Find the center and radius of the circle with equation (x + 3)^2 + (y – 6)^2 = 100.

Answer 1

Answer:

center         (-3,6)

radius(r)         10

Step-by-step explanation:

The center-radius form (it is really called standard form) of a circle is:

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

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

Compare the following:

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

$(x+3)^2+(y-6)^2=100$

You should see the following:

$-h=3$

$-k=-6$

$r^2=100$.

$-h=3 \text{ implies }h=-3$.

$-k=-6 \text{ implies } k=6$.

$r^2=100 \text{ implies } r=\sqrt{100}=10$.

So the center is (-3,6) and the radius is 10.