Chapter 11, Problem 13RE

To determine

To draw: the graph of the ellipse.

Explanation of Solution

Given information:

The equation of ellipse is $\frac{{\left(x-3\right)}^2}{9}+\frac{y^2}{16}=1$

Graph: to draw the graph of the ellipse, use the plotting point method,

$x$	$y$
$6$	$0$
$1$	$3$
$0$	$0$

By using the above table, and join the points,

The graph can be obtained as:

  

Interpretation: from the above graph it can be observed that the centre of the ellipse is $\left(3,0\right)$ , vertices are $\left(3,\pm 4\right)$ , foci are $\left(3,\pm \sqrt{7}\right)$ and the length of the major axis is $8$ and length of minor axis is $6$ .