The two points (2,4) and (9,4) are the endpoints of the diameter of a circle. what is the equation of this circle in standard form?

The midpoint of the diameter endpoints is the center of the circle...

((2+9)/2, (4+4)/2)

(5.5, 4) is the center of the circle...

The distance between the two endpoints is the diameter of the circle...

d^2=(4-4)^2+(9-2)^2

d^2=0+49

d^2=49

d=7

So the radius is d/2 which is 3.5

Now the equation of a circle is:

(x-h)^2+(y-k)^2=r^2  where (h,k) is the coordinates of the center and r is the radius.

Earlier we found (h,k) to be (5.5, 4) and r=3.5 so our equation is:

(x-5.5)^2+(y-4)^2=3.5^2

(x-5.5)^2+(y-4)^2=12.25