Question

A plot of land in the shape of a vertical ellipse has a pole at each focus. The foci are 8 feet from the center. If the plot of land is 34 feet across the vertical axis, then it is (A.24 B. 30 C. 32 D. 36) feet across the other axis. The eccentricity of the ellipse traced by the boundary of this plot, rounded to the nearest thousandth, is (A.0.543 B.0.515 C.0.471 D. 0.459)

Answer 1

Answer:

1. B

2.C

Step-by-step explanation:

A plot of land in the shape of a vertical ellipse. The equation of the ellipse is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1.$

If the foci are 8 feet from the center, then $c=8.$

If the plot of land is 34 feet across the vertical axis, then $2b=34\Rightarrow b=17.$

Use formula $c=\sqrt{b^2-a^2}$ (because ellipse is vertical, then b>a) to find a:

$8=\sqrt{17^2-a^2}\Rightarrow a^2=289-64=225,\ a=15.$

Then  the plot of land is 2a=30 ft across the other axis.

If b>a, the eccentricity of the ellipse is

$e=\dfrac{c}{b}=\dfrac{8}{17}\approx 0.471.$