Given the equation of a circle, determine the center and the radius.〖(x+5)〗2+〖(y-1)〗2=9.

the equation of a circle is (x-h)2 +(y-k)2 = r2

The center is (-5,1)

and

the radius is 3

Step-by-step explanation:

The given equation of the circle is

We can rewrite this equation in the form;

This implies that;

When we compare, we get;

(h,k)=(-5,1) which is the center and r=3 the radius.

The answer is:

The center of the circle is located on the point (-5,1) and the radius is equal to 3 units.

To determine the center and the radius of a circle from its equation, we need to look for "h" and "k", being "h" the x-coordinate of the center and "k" the y-coordinate the center, then, calculate the radius.

Since we are given the ordinary equation of the circle, we can find the radius and the center directly.

The ordinary equation is:

Where,

h is the x-coordinate of the center

y is the y-coordinate of the center

r is the radius.

So, we are given the circle:

Which is also equal to:

Where,

Hence, the center of the circle is located on the point (-5,1) and the radius is equal to 3 units.

Have a nice day!

the graph on the bottom right