StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q 60.

Expert-verifiedFound in: Page 655

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Find an equation for each ellipse. Graph the equation by hand.

Vertices at $(2,5)$ and $(2,-1)$:c=2

The equation of the ellipse is $\frac{{(x-2)}^{2}}{5}+\frac{{(y-2)}^{2}}{9}=1$and graph of the ellipse is

Vertices at $(2,5)$ and $(2,-1)$: $c=2$

The vertices lies on the line $x=2$, thus the major axis is parallel to the y-axis.

The center is at the mid point of the vertices $(2,2)$.

The distance of the center from one of the foci is $c=2$.

The distance of the center from one of the vertices is $a=3$.

Substitute $a=3$ and $c=2$ in ${b}^{2}={a}^{2}-{c}^{2}$ we get.

${b}^{2}={a}^{2}-{c}^{2}\phantom{\rule{0ex}{0ex}}{b}^{2}=9-4\phantom{\rule{0ex}{0ex}}{b}^{2}=5$

Substituting the values of ${a}^{2}$ and ${b}^{2}$ in the equation of the ellipse we get.

$\frac{{(x-2)}^{2}}{5}+\frac{{(y-2)}^{2}}{9}=1$

94% of StudySmarter users get better grades.

Sign up for free