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Q 62.

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.

Center at $(1,2)$: focus at $(1,4)$: contains the point $(2,2)$

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

Center at $(1,2)$: focus at $(1,4)$ contains the point$(2,2)$.

Since the center and the focus lie on the line $x=1$, thus the major axis is parallel to the y-axis.

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

Since, the point $(2,2)$ lies on the ellipse

$\frac{{(2-1)}^{2}}{{b}^{2}}+\frac{{(2-2)}^{2}}{{a}^{2}}=1\phantom{\rule{0ex}{0ex}}{b}^{2}=1$

Substitute $c=2$ and $a=1$ we get.

${b}^{2}={a}^{2}-{c}^{2}\phantom{\rule{0ex}{0ex}}{a}^{2}={b}^{2}+{c}^{2}\phantom{\rule{0ex}{0ex}}{a}^{2}=1+4\phantom{\rule{0ex}{0ex}}{a}^{2}=5$

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

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