Question

If there were only one pushpin used, what would be the shape of the ellipse?What would its eccentricity be?

Answer 1

Answer:

Circle

Eccentricity = 0

Explanation:

To draw an ellipse, we can use two pushpins and a string, so we will draw the ellipse as in the following figure:

Then, if we use only one pushpin, we will get a circle, because all the lines will be at the same distance from the pushpin

Therefore, the shape of the ellipse will be a circle.

The eccentricity of an ellipse is calculated as:

$e=\frac{\sqrt[]{a^2-b^2}}{a}$

Where a and b are the values shown in the following figure:

In a circle these values are equal, so we can replace b by a and get:

$e=\frac{\sqrt[]{a^2-a^2}}{a}=\frac{0}{a}=0$

Therefore, the eccentricity for a circle will be 0.