Chapter EP, Problem 10.4.3EP

To determine

To find: The equation of ellipse that satisfies each set of conditions.

Answer to Problem 10.4.3EP

The equation of ellipse is given below.

Explanation of Solution

Given:

The major axis is $24$ units long and parallel to the $y$ -axis.

The minor axis is $4$ units long.

The centre is $\left(0,3\right)$ .

The standard form of the equation of ellipse that is parallel to $y$ -axiswith centre $\left(h,k\right)$ and length of major axis is $2a$ and length of minor axis is $2b$ , is given as:

  $\frac{{\left(y-k\right)}^2}{a^2}+\frac{{\left(x-h\right)}^2}{b^2}=1$

The length of the major axis $2a$ is given as:

  $\begin{array}{c}2a=24\\ a=12\end{array}$

The length of the minor axis $2b$ is given as:

  $\begin{array}{c}2b=4\\ b=2\end{array}$

So the equation for the ellipse is given as:

  $\begin{array}{c}\frac{{\left(y-3\right)}^2}{{12}^2}+\frac{{\left(x-0\right)}^2}{2^2}=1\\ \frac{{\left(y-3\right)}^2}{144}+\frac{x^2}{4}=1\end{array}$