To identify the conic section represented by the equation \( y^2 - 3x + 4y + 7 = 0 \), we will rearrange it into a more recognizable form.
Starting from the original equation:
\[ y^2 + 4y - 3x + 7 = 0 \]
We can isolate the \(x\) term:
\[ 3x = y^2 + 4y + 7 \]
Divide through by 3:
\[ x = \frac{1}{3}y^2 + \frac{4}{3}y + \frac{7}{3} \]
This equation is in the form \(x = Ay^2 + By + C\), which represents a parabola in terms of \(y\).
Therefore, the conic section represented by the equation is:
parabola
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