Question

How do we graph this ellipse?

2x^2 + (y^2)/2 = 1

Answer 1

Let's get it into standard form.\[\large \left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2=1\]
Hmm, so the x has a 2 on it.
Multiplying by 2 is the same as dividing by 1/2.\[\large 2x^2 \qquad \rightarrow \qquad \frac{x^2}{\left(\frac{1}{2}\right)}\]Then let's apply the square to both the top and bottom term.\[\large \frac{x^2}{\left(\frac{1}{2}\right)} \qquad \rightarrow \qquad \left(\frac{x}{\frac{1}{\sqrt2}}\right)^2\]Now we can clearly see what our \(a\) value is.

Answer 2

Doing similar to the y gives us something like this I believe,
\[\large \left(\frac{x}{\frac{1}{\sqrt2}}\right)^2+\left(\frac{y}{\sqrt2}\right)^2=1\]

And then to graph it.. ummm trying to remember.
If x=0, y extends out to \(\pm \sqrt2\).
if y=0, x extends out to \(\pm \dfrac{1}{\sqrt2}\)