Claire is looking at the equation of a conic section where a=1, b=0, c=0. which type of conic section is represented by the equation?

The general equation of second degree is
                             Ax²+By²+Gx+Fy+C=0 1

Now the given conditions are 
A=1, B=0, C=0
Now,
putting in eq. 1
x²+Gx+Fy=0
x²+Gx= -Fy
For completing square, add both side (G/2)²
x²+Gx+(G/2)²=-Fy+(G/2)²
(x+G/2)²=-F(y-G²/4F)
Or
X²=-FY where X=x+G/2, Y=y-G²/4F
which is the standard eq. of parabola in XY-coordinate.