Question

the eccentricity of the ellipse is approximately Choose... : 0.57, 0.87, 1.15 . This value indicates that the ellipse is more Choose... : circular then elongated, elongated then circular.

Answer 1

Solution

- The eccentricity of an ellipse is given below:

$\begin{gathered} Given\text{ the ellipse:} \\ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\ \\ \text{ The eccentricity is:} \\ e=\sqrt{1-\frac{b^2}{a^2}} \\ \\ \text{ From the equation given,} \\ a^2=49,b^2=12 \\ \\ e=\sqrt{1-\frac{12}{49}} \\ \\ e=0.868966...\approx0.87 \end{gathered}$

- The eccentricity is 0.87

- Because the eccentricity is close to 1, it means it is flatter than normal. Thus, it is "elongated then circular"

Final Answer

- The eccentricity is 0.87

- "elongated then circular"