Question

What is the equation of this circle in standard form M(2,4) N(9,4) these are coordinates across the diameter of the circle?

Answer 1

The standard form is

(x-xo)² + (y-yo)² = r²

Where xo,yo is the center of the circumference
and r is the radius.

We find the distance between the points to determine the diameter

d=sqrt ((9-2)² + (4-4)²) = sqrt (49) = 7

The radius of the circumference is d/2 = 7/2 = 3.5

And we can see that those points are at the same coordinate y = 4 

The center is given then by , x = (9+2)/2 = 5.5
                                              y = (4+4)/2 = 4

The equation results

(x-5.5)² + (y-4)² = (3.5)²