+1911 Help I don't know how to graph circles
The equation of a circle in the coordinate plane can be written as $Ax^2 + 2y^2 + Bx + Cy = 50.$ The center of the circle is at $(-5,2)$. Let $r$ be the radius of the circle. Find $A+B+C+r.$
+129852 The center is (-5, 2)
So we have that
( x + 5)^2 + (y - 2)^2 = r^2 simplify
x^2 + 10x + 25 + y^2 - 4y + 4 = r^2
x^2 + y^2 + 10x - 4y = r^2 - 29 multipy through by 2
2x^2 + 2y^2 + 20x - 8y = 2r^2 -58
A = 2 B = 20 C = -8
And we know that
2r^2 - 58 = 50 divide through by 2
r^2 - 29 = 25
r^2 = 54
r =sqrt (54)
A + B + C + r = 2 + 20 - 8 + sqrt (54) = 14 + sqrt (54) = 14 + sqrt (9 * 6) = 14 + 3 sqrt (6)
