Chapter 9, Problem 27CR

To determine

To graph: the ellipse.

Explanation of Solution

Given information:

The ellipse equation is $\frac{x^2}{25}+\frac{y^2}{36}=1$ .

Graph: to draw the graph of the ellipse, first write the ellipse in the standard form,

  $\begin{array}{l}\frac{x^2}{25}+\frac{y^2}{36}=1\\ \frac{x^2}{{\left(5\right)}^2}+\frac{y^2}{{\left(6\right)}^2}=1\end{array}$

Form the equation, the centre of the ellipse is $\left(0,0\right)$ .

Because the denominator of the $y^2$ -term is greater than the denominator of the $x^2$ -term, so the major axis of the ellipse is vertical.

Therefore $a=6$ and the vertices are $\left(0,-6\right)\text{ and }\left(0,6\right)$ .

And from the equation $b=5$ , thus the endpoints of the minor axis are $\left(-3,0\right)\text{ and }\left(3,0\right)$ .

So by using the above data, the graph of ellipse can be obtained as:

  

Interpretation: from the above graph it can be observed that the centre of the ellipse is $\left(0,0\right)$ , vertices are $\left(0,\pm 6\right)$ , foci is $\left(0,\pm \sqrt{11}\right)$ and eccentricity is $\frac{\sqrt{11}}{6}$ .