Question

does anyone know the general form equation of a circle with a center (4,5) that passes through (-1,2)

...and just checking, would the standard form equation be:
(-1+4)^2 + (2+5)^2 = 58

Answer 1

No, the general equation would involve x and y variables. First get the radius of the circle from the distance between th center and the other point. That distance is
R = sqrt[4 -(-1)]^2 + (5-2)^2] = sqrt 34

The equation is
(x-x')^2 + (y-y')^2 = 34

where x' and y' are the coordinates of the center, 4 and 5.

(x-4)^2 + (y-5)^2 = 34

Answer 2

so the general form equation is
(x-4)^2 + (y-5)^2 = 34 ?
then what is the standard form?

Answer 3

General and standard form mean the same thing to me. The equation I wrote is for the specific circle that the problem asked for.