Chapter 11.4, Problem 20E

To determine

To find: an equation for the conic

Answer to Problem 20E

The equation is $\frac{{\left(x-2\right)}^2}{4}+\frac{{\left(y+3\right)}^2}{9}=1$

Explanation of Solution

Given information: The graph provided in the question shown below

  

Calculation: General equation of ellipse

  $\begin{array}{l}\frac{{\left(x-h\right)}^2}{a^2}+\frac{{\left(y-k\right)}^2}{b^2}=1\\ center:\left(h,k\right)=\left(2,-3\right)\\ \frac{{\left(x-2\right)}^2}{a^2}+\frac{{\left(y+3\right)}^2}{b^2}=1\end{array}$

Major axis $=2b=6\Rightarrow b=3$

Minor axis $=2a=4\Rightarrow a=2$

So, the final equation is $\frac{{\left(x-2\right)}^2}{4}+\frac{{\left(y+3\right)}^2}{9}=1$