Question

Identify the conic section represented by the equation y squared minus 3 x plus 4 y plus 7 equals 0.
(1 point)
Responses

circle
circle

ellipse
ellipse

parabola
parabola

hyperbola

Answer 1

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**