Question

I need this practice problem answered Here are the answer options:The eccentricity of the ellipse is approximatelyA. 0.71B. 0.91C. 1.10This value indicates that the ellipse is moreA. Circular then elongated B. Elongated than circular

Answer 1

The eccentricity is the measure of how much the ellipse deviates from a circle.

The eccentricity of an ellipse which is not a circle is greater than zero but less than 1.

For an ellipse, the eccentricity is giving as

`\frac{\sqrt[]{a^2-b^2}}{a}`

where

`\begin{gathered} a^2=50,a=\sqrt[]{50}=5\sqrt[]{2} \\ b^2=9,b=\sqrt[]{9}=3 \end{gathered}`

Substitute the value into the formula we have

`\begin{gathered} \frac{\sqrt[]{50-9}}{5\sqrt[]{2}} \\ \text{Then } \\ \frac{\sqrt[]{41}}{5\sqrt[]{2}} \end{gathered}`

Then rationalize the expression in the last line

`\frac{\sqrt[]{41}*\sqrt[]{2}}{5\sqrt[]{2}*\sqrt[]{2}}=\frac{\sqrt[]{82}}{10}=0.9055`

Hence the eccentricity of the ellipse is approximately 0.91

Since the value of a is much larger than b, then it indicates that the ellipse is

More Elongated than circular.