Question

a circle is represented by the equation below: (x + 2)^2+(y - 4)^2 = 225. which statement is true? the circle is centered at (-2, 4) and has a radius of 15. the circle is centered at (2, -4) and has a diameter of 15. the circle is centered at (2, -4) and has a radius of 15. the circle is centered at (-2, 4) and has a diameter of 15.

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle's equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.

Step2: Identify the center

For the equation $(x + 2)^2+(y - 4)^2 = 225$, we have $x+2=x-(-2)$ and $y - 4$ as is. So the center $(a,b)=(-2,4)$.

Step3: Identify the radius

Since $r^2 = 225$, then $r=\sqrt{225}=15$.

Answer:

The circle is centered at $(-2,4)$ and has a radius of $15$.