Answer:
The diameter is 10 units.
The equation of the circle is [tex](x-6)^2+y^2=25[/tex].
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.
[tex]d=\sqrt{(6-2)^2+(0-(-3))^2}[/tex]
[tex]d=\sqrt{(4)^2+(3)^2}[/tex]
[tex]d=\sqrt{16+9}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]d=5[/tex]
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
[tex](x-6)^2+(y-0)^2=5^2[/tex].
You are probably wondering how I got that. I used the center-radius form for a circle which is [tex](x-h)^2+(y-k)^2=r^2[/tex].
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:
[tex](x-6)^2+y^2=25[/tex].
All I did was y-0 which is y and 5^2 which is 5(5) which equals 25.
