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### 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. 