Chapter 11, Problem 26RE

To determine

To find: The equation of the conic when graph is given.

Answer to Problem 26RE

Equation of the conic is $\frac{x^2}{144}+\frac{y^2}{25}=1$

Explanation of Solution

Given information:

Graph of conic is given.

  

Calculation:

By looking at the conic we can tell that it is an ellipse.

Center of the ellipse is at $\left(0,0\right)$

Length of the major axis $\Rightarrow 24$ , according to the graph.

Length of the minor axis $\Rightarrow 10$ , according to the graph

Given, ellipse is horizontal ellipse.

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

Center $\Rightarrow \left(h,k\right)$

As major axis is on the x − axis,

  $\to 2a$ will be the length of x − axis.

  $\to 2b$ will be the length of the major axis.

Here,

  $\begin{array}{l}2a=242b=10\\ a=12b=5\\ \left(h,k\right)=\left(0,0\right)\end{array}$

Thus, the Equation of ellipse $\Rightarrow \frac{x^2}{144}+\frac{y^2}{25}=1$