Question

the equation of a circle is given below. identify the radius and center.
$(x + 5)^2+(y - 4)^2=9$

Explanation:

Step1: Recall the standard - form of a circle equation

The standard - form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.
For the given equation $(x + 5)^2+(y-4)^2 = 9$, we can rewrite it as $(x-(-5))^2+(y - 4)^2=3^2$.

Step2: Identify the center and radius

Comparing with the standard form, the center of the circle is $(a,b)=(-5,4)$ and the radius $r = 3$.

Answer:

Center: $(-5,4)$; Radius: $3$