Chapter 11.4, Problem 21E

To determine

To find: an equation for the conic

Answer to Problem 21E

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

Explanation of Solution

Given information: The graph provided in the question shown below

  

Calculation: General equation of ellipse

  $\begin{array}{l}\frac{{\left(y-k\right)}^2}{a^2}-\frac{{\left(x-h\right)}^2}{b^2}=1\\ a=2\\ center:\left(h,k\right)=\left(2,-3\right)\\ y=k\pm \frac{a}{b}\left(x-h\right)\\ y=1\pm \frac{2}{6}\left(x\right)\\ y=x+1\Rightarrow 1+\frac{2x}{b}\\ b=2\\ \frac{{\left(y-1\right)}^2}{2^2}-\frac{x^2}{2^2}=1\end{array}$

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