Will mark as brainliest if correct and explained
what is the diameter of the circle whose center is at (6, 0) and that passes through the point (2, -3)?
a. (x+16)2+(y+30)2=1156
b. (x+16)2+(y+30)2=34
c. (x−16)2+(y−30)2=34
d. (x−16)2+(y−30)2=1156

The diameter is 10 units.

The equation of the circle is .

Step-by-step explanation:

You ask for the diameter but the choices give you the equation of the circle?

I will do both.

So they actually tell us the radius is from (6,0) to (2,-3).

So the radius is whatever that length is.  We can find the length by using the distance formula.

So the radius is 5.

The diameter is twice the radius so the diameter is 2(5)=10.

Now the equation of our circle which doesn't match any of the choices is

.

You are probably wondering how I got that.  I used the center-radius form for a circle which is .

The center is (h,k) and the radius is r.

We had the center for our circle was (6,0) and the radius was 5.

I'm going to simplifying our equation just a bit:

.

All I did was y-0 which is y and 5^2 which is 5(5) which equals 25.