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Q. 102

Expert-verifiedFound in: Page 1118

Book edition
OER 2017

Author(s)
OPENSTAX

Pages
1346 pages

ISBN
9780998625720

In the following exercises, graph each ellipse.

$\frac{{x}^{2}}{16}+\frac{{y}^{2}}{36}=1.$

The graph of the ellipse is

The equation of the ellipse is$\frac{{x}^{2}}{16}+\frac{{y}^{2}}{36}=1.$

The standard form of the ellipse with

$\text{Centre:}\left(0,0\right)\text{is}$

$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1\phantom{\rule{0ex}{0ex}}a>b\Rightarrow \text{major axis is}x-\text{axis with end points}\left(-a,0\right)\text{,(a,0)}\phantom{\rule{0ex}{0ex}}b>a\Rightarrow \text{major axis is}y-\text{axis. with end points}\left((0,-b\right)\text{,(0,b)}$$\frac{{x}^{2}}{16}+\frac{{y}^{2}}{36}=1$

Compare with the standard form of the ellipse

localid="1645432640134" $\text{Center}\left(0,0\right)\text{,}\phantom{\rule{0ex}{0ex}}36>16\text{and}\phantom{\rule{0ex}{0ex}}{a}^{2}=16\Rightarrow a=\pm 4\phantom{\rule{0ex}{0ex}}{b}^{2}=36\Rightarrow b=\pm 6$

__Major axis: __

Onlocalid="1645425899245" $y-\text{axis}$ with endpoints $(0,-6),(0,6).$

__Minor axis:__

Onlocalid="1645426041274" $x-\text{axis with endpoints}\left(-4,0),(0,4\right)\text{.}$

The graph of the ellipse is

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