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

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(39623) (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.

as given.

The missing square term for x and for y are, in that order, and . This will allow you to factor.

According to that standard form equation for a circle, the center is at (-g,-f) and the radius is .

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