Question

determine if $-2x^2 + y = 1$ is an ellipse.
\bigcirc not an ellipse
\bigcirc ellipse, we can write the equation of the ellipse in standard form $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$.
where:
$h = \square$
$k = \square$
$a = \square$
$b = \square$
question help: \video video 1 \video video 2 \message message instructor

Explanation:

Step1: Recall the standard form of an ellipse

The standard form of an ellipse is \(\frac{(x - h)^{2}}{a^{2}}+\frac{(y - k)^{2}}{b^{2}}=1\) (\(a\gt0,b\gt0\)), which has both \(x^{2}\) and \(y^{2}\) terms with positive coefficients.

Step2: Analyze the given equation \(-2x^{2}+y = 1\)

Rewrite it as \(y=2x^{2}+1\). This is a parabola (in the form \(y = ax^{2}+bx + c\) with \(a = 2
eq0\)), not an ellipse since it lacks a \(y^{2}\) term in the form required for an ellipse.

Answer:

Not an Ellipse