Question 162033
Notice how there is no {{{y^2}}} term. So this means that the equation is NOT a circle, ellipse, or hyperbola. So it's either a line or a parabola. However, let's use some algebra to find out for sure.


{{{9x^2 - 3 = 18x + 4y}}} Start with the given equation



{{{9x^2 - 3-18x = 4y}}} Subtract 18x from both sides



{{{9x^2 -18x- 3 = 4y}}} Rearrange the terms 



{{{4y=9x^2 -18x- 3}}} Rearrange the equation



{{{y=(9x^2 -18x- 3)/4}}} Divide both sides by 4 to isolate "y"



{{{y=(9x^2)/4 -(18x)/4- (3)/4}}} Break up the fraction



{{{y=(9/4)x^2 -(9/2)x- 3/4}}} Reduce



So this equation fits the general second degree polynomial which means that it is a parabola. If we graph {{{y=(9/4)x^2 -(9/2)x- 3/4}}}, we get


{{{ graph( 500, 500, -10, 10, -10, 10, (9/4)x^2 -(9/2)x- 3/4) }}}  Graph of {{{y=(9/4)x^2 -(9/2)x- 3/4}}}


So this confirms our answer.