Equation for given circle. A (4,7) is at center top of circle and B (7,4) is at center right hand side

Note:

The equation for a circle with center at (h, k) and radius r is

(x-h) ² + (y-k) ² = r²

For the specified circle,

h=4, h=7.

From the diagram shown below, the radius, r, is determined from the Pythagorean Theorem as

r² = 3² + 3² = 18

Therefore the equation for the circle is

(x - 4) ² + (y - 7) ² = 18

Answer: (x - 4) ² + (y - 7) ² = 18