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Answers without the blur. Sign up and see all textbooks for free! Q. 102

Expert-verified Found in: Page 1118 ### Intermediate Algebra

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 See the step by step solution

## Step 1. Given information

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

## Step 2. Concept used

The standard form of the ellipse with

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

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

## Step 3. Find the center and major axis

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

Compare with the standard form of the ellipse

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

Major axis:

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

Minor axis:

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

## Step 4. Graph the ellipse

The graph of the ellipse is  ### Want to see more solutions like these? 