Question

What is the equation of this circle in standard form?

Answer 1

The general equation of a circle in standard form is:
(x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center and r is the radius.
So we need to find the center of the circle and the radius of the circle.

The center of the circle is the midpoint of M and N. Find the midpoint.
The radius of the circle is half the distance between M and N.

Answer 2

I still cant figure out if It's A,C, or E

Answer 3

Midpoint of MN = ( (2+9)/2 , (4+4)/2 ) = (5.5, 4)
So the center of the circle is (5.5, 4). Compare it to the general form and we have h = 5.5 and k = 4.

The distance between M and N is: 9 - 2 = 7. Therefore, the radius is: 7/2 = 3.5.

Put h = 5.5, k = 4 and r = 3.5 in (x - h)^2 + (y - k)^2 = r^2

Answer 4

thank you so much, I think I understand now! Is the answer E?

Answer 5

Yes. You are welcome.