precalc
posted by Melissa on .
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

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 + (52)^2] = sqrt 34
The equation is
(xx')^2 + (yy')^2 = 34
where x' and y' are the coordinates of the center, 4 and 5.
(x4)^2 + (y5)^2 = 34 
so the general form equation is
(x4)^2 + (y5)^2 = 34 ?
then what is the standard form? 
General and standard form mean the same thing to me. The equation I wrote is for the specific circle that the problem asked for.