Find the length of a radius of the circle. 64 x 2 + 64 y 2 $-$ 16 x $-$ 112 y $-$ 2,446 = 0
A) $r = 1,521$
B) $r = 1$
C) $r = \sqrt { 39 }$
D) $r = 3 \sqrt { 39 }$
E) $r = 39$

Question

Quizplus · Accepted Answer

We want to write the given equation in the standard form of the equation of a circle, which is:
$$(x-a)^2 + (y-b)^2 = r^2$$
where $(a,b)$ is the center of the circle and $r$ is its radius.

To do this, we complete the square for both variables:

\begin{align*}
64x^2 + 64y^2 - 16x -112y -2446 &= 0 \
64(x^2 - \frac{1}{4}x) + 64(y^2 - \frac{7}{8}y) &= 2446 \
64(x^2 - \frac{1}{4}x + \frac{1}{16}) + 64(y^2 - \frac{7}{8}y + \frac{49}{64}) &= 2446 + 1 + 49 \
64(x - \frac{1}{4})^2 + 64(y - \frac{7}{16})^2 &= 2496 \
(x - \frac{1}{4})^2 + (y - \frac{7}{16})^2 &= 39 \
\end{align*}

So the center of the circle is $\left(\frac{1}{4},\frac{7}{16}ight)$ and the radius is $r = \sqrt{39}$. Therefore, the best choice is C.

Find the Length of a Radius of the Circle −-− 16 X

Find the Length of a Radius of the Circle $-$ 16 X