Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises: 54

Answer

The intercepts with $y$ axis are $y=1$ and $y=-1$. The intercepts with $x$ axis are $x=2$ and $x=-2$. The graph is symmetric with respect to both $x$ and $y$ axis and is shown on the figure.
1492791141

Work Step by Step

To find the intercepts with $y$ axis put $x=0$ and calculate $y$: $$0^2+4y^2 = 4\Rightarrow 4y^2=4\Rightarrow y^2=1\Rightarrow y=\pm 1$$ so there are two intercepts with $y$ axis $y=1$ and $y=-1$. To find the intercept with $x$ axis put $y=0$ and calculate $x$: $$x^2+4\times0^2=4\Rightarrow x^2=4\Rightarrow x=\pm2$$ so there are also two intercepts with the $x$ axis $x=2$ and $x=-2$. The graph is symmetric with respect to both $y$ and $x$ axis because if we put $-y$ instead of $y$ or $-x$ instead of $x$ we obtain the starting equation: $$(-x)^2+4y^2=x^2+4y^2=4.$$ $$x^2+4(-y)^2 = x^2+4y^2=4.$$
Small 1492791141
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.