Question

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

Answer 1

Answer:

The center is (-5,1)

and

the radius is 3

Step-by-step explanation:

The given equation of the circle is

$(x+5)^2+(y-1)^2=9$

We can rewrite this equation in the form;

$(x-h)^2+(y-1)^2=r^2$

This implies that;

$(x--5)^2+(y-1)^2=3^2$

When we compare, we get;

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

Answer 2

Hello!

The answer is:

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

Why?

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:

$(x-h)^{2} +(y-k)^{2} =r^{2}$

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:

$(x+5)^{2} +(y-1)^{2} =9$

Which is also equal to:

$(x-(-5))^{2} +(y-(1))^{2} =9$

Where,

$h=-5\\k=1$

$r^{2}=9\\\sqrt{r^{2}}=\sqrt{9} \\r=3units$

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!