What is "a circle has its center at (1?

, -2) and passes through the point (5, 4)"

A circle with center at (1, -2) and passing through the point (5, 4) can be represented by the equation:

(x-1)^2 + (y+2)^2 = r^2

where r is the radius of the circle.

To find the radius, we can use the distance formula between the center and the point on the circle:

r = sqrt((5-1)^2 + (4-(-2))^2) = sqrt(36 + 36) = 6sqrt(2)

Therefore, the equation of the circle is:

(x-1)^2 + (y+2)^2 = 72

We can also conclude that the diameter of the circle is 12sqrt(2) and the circumference is 12sqrt(2) pi.