Question

The equation of a circle, C, is x^2 + y^2 + 6x - 8y +9=0. Find the center of C and find the radius of C. Show that the C touches the x-axis. Find the equation of the circle which is a reflection of C in the y-axis

Answer 1

x^2+y^2+6x-8y+9 = 0
rearrange things a bit to get ready to complete the squares:
x^2+6x + y^2-8y = -9
x^2+6x+9 + y^2-8y+16 = -9+9+16
(x+3)^2 + (y-4)^2 = 16

so, the center is at (-3,4) with radius 4.

Note that the center is 4 units above the x-axis, so C touches the x-axis at (-3,0)

To reflect the circle in the y-axis, just flip the center to (+3,4). That makes the equation

(x-3)^2 + (y-4)^2 = 16

take a peek here:

http://www.wolframalpha.com/input/?i=plot+%28x%2B3%29^2+%2B+%28y-4%29^2+%3D+16%2C+%28x-3%29^2+%2B+%28y-4%29^2+%3D+16%2C+y%3D0%2C+x%3D0