Chapter 9.7, Problem 2MRE

To determine

To calculate: To find the equation of ellipse

Answer to Problem 2MRE

Equation of ellipse is $\frac{x^2}{6}+\frac{y^2}{4}=1$

Explanation of Solution

Given information: Ellipse with x-intercepts $\pm \sqrt{6}$ and y-intercepts $\pm 2$

Formula Used:

Standard form of the equation of ellipse is:

  $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Where, $a=$ x-intercept, $b=$ y-intercept

Calculation:

Given an ellipse with x-intercepts $\pm \sqrt{6}$ and y-intercepts $\pm 2$

  $\begin{array}{l}a=\pm \sqrt{6}\\ b=\pm 2\end{array}$

Standard form of the equation of ellipse is given as follows:

  $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Substituting the values:

  $\begin{array}{l}\frac{x^2}{{\left(\pm \sqrt{6}\right)}^2}+\frac{y^2}{{\left(\pm 2\right)}^2}=1\\ \frac{x^2}{6}+\frac{y^2}{4}=1\end{array}$

Conclusion:

Hence, equation of ellipse is $\frac{x^2}{6}+\frac{y^2}{4}=1$