Chapter A5.1, Problem 17E

To determine

To sketch:the ellipse

Answer to Problem 17E

The ellipse’s focus is:

Focus: $\begin{array}{l}c=\sqrt{a^2-b^2}\Rightarrow c=3\\ \left(\pm c,0\right)\Rightarrow \left(\pm 3,0\right)\end{array}$

The sketch of the ellipse is:

  

Explanation of Solution

Given:

  $16x^2+25y^2=400$

Calculation:

The given equation is-

  $16x^2+25y^2=400\Rightarrow \frac{x^2}{25}+\frac{y^2}{16}=1$

Focus: $\begin{array}{l}c=\sqrt{a^2-b^2}\Rightarrow c=3\\ \left(\pm c,0\right)\Rightarrow \left(\pm 3,0\right)\end{array}$

Following is the sketch of the ellipse:

  

Conclusion:

The ellipse’s focus is:

Focus: $\begin{array}{l}c=\sqrt{a^2-b^2}\Rightarrow c=3\\ \left(\pm c,0\right)\Rightarrow \left(\pm 3,0\right)\end{array}$

The sketch of the ellipse is: