To determine which conic section is represented by the equation \(3x^2 - 6x - y + 5 = 0\), we can rearrange it into a more standard form.
Starting with the original equation:
\[ 3x^2 - 6x - y + 5 = 0 \]
We can isolate \(y\):
\[ y = 3x^2 - 6x + 5 \]
Now, observe that the equation is in the form \(y = ax^2 + bx + c\), where \(a = 3\), \(b = -6\), and \(c = 5\). This is the standard form of a quadratic equation in \(x\).
Since the equation features a squared term in \(x\) and not in \(y\), it indicates that this is a parabola.
So, the correct answer is:
parabola
1 answer