Write the standard form of the equation of the circle with the given center and radius. Center $$ (4,8), \mathrm{r}=5 $$ Type the standard form of the equation of the circle. $$ \square $$ (Simplify your answer.)

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The standard form of the equation of a circle with center $$(h, k)$$ and radius $$r$$ is given by:

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

For the given center $$(4, 8)$$ and radius $$r = 5$$, we can substitute $$h = 4$$, $$k = 8$$, and $$r = 5$$ into the equation:

$$
(x - 4)^2 + (y - 8)^2 = 5^2
$$

Calculating $$5^2$$:

$$
5^2 = 25
$$

Thus, the equation becomes:

$$
(x - 4)^2 + (y - 8)^2 = 25
$$

So, the standard form of the equation of the circle is:

$$
\boxed{(x - 4)^2 + (y - 8)^2 = 25}
$$
$$(x - 4)^2 + (y - 8)^2 = 25$$

Write the standard form of the equation of the circle with the given center and radius. Center \( (4,8), \mathrm{r}=5 \) Type the standard form of the equation of the circle. \( \square \) (Simplify your answer.)

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