Identify the center and radius of the circle $9 x ^ { 2 } + 9 y ^ { 2 } - 16 = 0$ .
A)center: (3,3) radius: 4
B)center: (0,0) radius: $ \frac{4}{3} $
C)center: (0,0) radius: $\frac { 3 } { 4 }$
D)center: (0,4) radius: $\frac { 1 } { 3 }$
E)center: (0,4) radius: $\frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

The equation of the circle is given in the form $9x^2 + 9y^2 - 16 = 0$. To find the center and radius, we can rewrite this equation in the standard form $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Dividing the given equation by 9 to simplify, we get $x^2 + y^2 = \frac{16}{9}$. This shows the center is at (0,0) and the radius is $\sqrt{\frac{16}{9}} = \frac{4}{3}$.

Identify the Center and Radius of the Circle 9x2+9y2−16=09 x ^ { 2 } + 9 y ^ { 2 } - 16 = 09x2+9y2−16=0

Identify the Center and Radius of the Circle $9 x ^ { 2 } + 9 y ^ { 2 } - 16 = 0$