What type is the curve and sketch the graph. Do not plot points. 4x^2 + y^2 = 1 I know it's an ellipse, but how do I tell how tall and how wide it should be??

Question

What type is the curve and sketch the graph.  Do not plot points.  4x^2 + y^2 = 1   I know it's an ellipse, but how do I tell how tall and how wide it should be??

anonymous · Answer

Compare to the general formula for an ellipse:
$$\left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2=1$$
$a$ is the length of the horizontal "radius" and $b$ is the length of the vertical "radius".

anonymous · Answer

Should I do anything with the 4?

anonymous · Answer

so it would be x= 1/4 and -1/4 and y = 1, -1. for the edges of the ellipse?

anonymous · Answer

My book is saying that it should be 1/2 instead of 1/4th?

anonymous · Answer

Sorry, I mean $a^2=\dfrac{1}{4}$, which means $a=\dfrac{1}{2}$.

anonymous · Answer

OH, perfect sense now

jdoe0001 · Answer

$\bf \cfrac{(x-h)^2}{a^2}+\cfrac{(y-k)^2}{b^2}=1\
-------------\
4x^2 + y^2 = 1 \implies \cfrac{(x-0)^2}{\frac{1}{4}}+\cfrac{(y-0)^2}{1} = 1$