Question

Identify the conic section represented by the equation y^2 - 3x + 4y +7 = 0 .
(1 point)
circle
ellipse
parabola
hyperbola

Answer 1

To identify the conic section represented by the equation \( y^2 - 3x + 4y + 7 = 0 \), we can rearrange it into a standard form.

Starting with the given equation:

\[
y^2 + 4y - 3x + 7 = 0
\]

We can isolate \( x \):

\[
3x = y^2 + 4y + 7
\]

\[
x = \frac{1}{3}(y^2 + 4y + 7)
\]

Next, let's analyze the form of the equation. In this equation, \( x \) is expressed as a function of \( y \), and it involves \( y^2 \) (which indicates that \( y \) is being squared).

Since this equation can be put into the form \( x = ay^2 + by + c \), where there is a squared term of \( y \) and the other terms are linear in \( y \), it is indicative of a parabola.

Thus, the conic section represented by the equation \( y^2 - 3x + 4y + 7 = 0 \) is:

**Parabola**