Chapter A5.1, Problem 18E

To determine

To sketch: the ellipse

Answer to Problem 18E

The ellipse’s focus is:

Focus: $\begin{array}{l}c=\sqrt{a^2-b^2}\Rightarrow c=1\\ \left(0,\pm c\right)\Rightarrow \left(0,\pm 1\right)\end{array}$

The sketch of the ellipse is:

  

Explanation of Solution

Given:

  $3x^2+2y^2=6$

Calculation:

The given equation is-

  $3x^2+2y^2=6\Rightarrow \frac{x^2}{2}+\frac{y^2}{3}=1$

Focus: $\begin{array}{l}c=\sqrt{a^2-b^2}\Rightarrow c=1\\ \left(0,\pm c\right)\Rightarrow \left(0,\pm 1\right)\end{array}$

Following is the sketch of the ellipse:

  

Conclusion:

The ellipse’s focus is:

Focus: $\begin{array}{l}c=\sqrt{a^2-b^2}\Rightarrow c=1\\ \left(0,\pm c\right)\Rightarrow \left(0,\pm 1\right)\end{array}$

The sketch of the parabola is: