Section 1.10 : Common Graphs
15. Without using a graphing calculator sketch the graph of \(\displaystyle 25{\left( {x + 2} \right)^2} + \frac{{{y^2}}}{{4}} = 1\).
Show Solution
This is just an ellipse that is almost in standard form. With a little rewrite we can put it into standard form as follows,
\[\frac{{{\left( x+2 \right)}^{2}}}{{}^{1}/{}_{25}}+\frac{{{y}^{2}}}{4}=1\]We can now see that the ellipse has a center of \(\left( { - 2,0} \right)\) while the left/right most points will be \(\frac{1}{5} = 0.2\) units away from the center and the top/bottom most points will be 2 units away from the center. Here is a quick sketch of the ellipse.
