## Related questions with answers

* Comet Orbit* Halley’s comet has an elliptical orbit, with the sun at one focus. The eccentricity of the orbit is approximately $0.967$. The length of the major axis of the orbit is approximately $35.88$ astronomical units. (An astronomical unit is about $93$ million miles.)

Find an equation of the orbit. Place the center of the orbit at the origin, and place the major axis on the $x$-axis.

Solution

VerifiedGiven:

$\begin{aligned} e&=\text{Eccentricity}=0.967 \\ 2a&=\text{Length major axis}=35.88\text{ astronomical units} \end{aligned}$

We need to determine an equation for the ellipse, assuming that the origin corresponds with the center and the major axis is horizontal.

Standard form of the equation of an ellipse ($0<b<a$):

$\begin{aligned} \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}&=1 &\textcolor{#4559AC}{\text{Horizontal major axis}} \\ \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}&=1 &\textcolor{#4559AC}{\text{Vertical major axis}} \end{aligned}$

- The length of the major axis is $2a$.
- Center is $(h,k)$
- Eccentricity: $e=\frac{c}{a}$ with $c^2=a^2-b^2$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Thomas' Calculus

14th Edition•ISBN: 9780134438986Christopher E Heil, Joel R. Hass, Maurice D. Weir#### Calculus I with Precalculus

3rd Edition•ISBN: 9780840068330 (4 more)Bruce E. Edwards, Ron Larson#### Calculus: Early Transcendentals

8th Edition•ISBN: 9781285741550 (2 more)James Stewart#### Calculus: Early Transcendentals

9th Edition•ISBN: 9781337613927 (2 more)Daniel K. Clegg, James Stewart, Saleem Watson## More related questions

- economics

1/4

- economics

1/7