SOLUTION: Under what conditions does the equation x^2 + y^2 + 2gx + 2fy +c = 0 represent a circle 1.with center on a) x axis b) y axis c) x and y axis Can you please help me out? T

Algebra ->  Circles -> SOLUTION: Under what conditions does the equation x^2 + y^2 + 2gx + 2fy +c = 0 represent a circle 1.with center on a) x axis b) y axis c) x and y axis Can you please help me out? T      Log On


   

Question 792682: Under what conditions does the equation x^2 + y^2 + 2gx + 2fy +c = 0 represent a circle
1.with center on
a) x axis
b) y axis
c) x and y axis
Can you please help me out? Thanks so much in advance:)
Can you also please show the steps it would really help me understand better:)
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Mostly a conic-section concept and symbolism exercise. First, you want to Complete-the-Square for the x and the y, and convert the equation to standard form. You will obtain something a little complicated, but you can use the formula.

x%5E2+%2B+y%5E2+%2B+2gx+%2B+2fy+%2Bc+=+0 as given.
x%5E2%2B2gx%2By%5E2%2B2fy%2Bc=0
The missing square term for x and for y are, in that order, %282g%2F2%29%5E2=g%5E2 and %282f%2F2%29%5E2=f%5E2. This will allow you to factor.
%28x%5E2%2B2gx%2Bg%5E2%29%2B%28y%5E2%2B2fy%2Bf%5E2%29%2Bc-g%5E2-f%5E2=0
highlight%28%28x%2Bg%29%5E2%2B%28y%2Bf%29%5E2=g%5E2%2Bf%5E2-c%29

According to that standard form equation for a circle, the center is at (-g,-f) and the radius is sqrt%28g%5E2%2Bf%5E2-c%29.

You should now be able to work through to the necessary conclusions.