Question

In the following exercise, graph the equation$\frac{{\left(x-2\right)}^2}{9}+\frac{{\left(y+3\right)}^2}{25}=1$

Short answer

The required equation of a curve and graph is as follows

Step-by-step solution

Step 1, Given the information   

The given equation of the curve$\frac{{\left(x-2\right)}^2}{9}+\frac{{\left(y+3\right)}^2}{25}=1$

Step 2. Draw a graph  

The standard equation of the ellipse is $\frac{{\left(x-2\right)}^2}{9}+\frac{{\left(y+3\right)}^2}{25}=1$

Since, $9<25$the major axis be vertical

Therefore, $$\begin{gathered} b^2=9 \\ b=\pm 3 \end{gathered}$$and $$\begin{gathered} a^2=25 \\ a=\pm 5 \end{gathered}$$

center of the ellipse is $\left(2,-3\right)$