Suggested languages for you:

Americas

Europe

Q 67.

Expert-verifiedFound in: Page 655

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Graph each function.

$f\left(x\right)=-\sqrt{64-16{x}^{2}}$

The graph of the function is half an ellipse.

WE have given function is $y=-\sqrt{64-16{x}^{2}}$.

Now, find an equation of conic, we have

${y}^{2}=64-16{x}^{2}\phantom{\rule{0ex}{0ex}}{y}^{2}+16{x}^{2}=64\phantom{\rule{0ex}{0ex}}\frac{{y}^{2}}{64}+\frac{{x}^{2}}{4}=1\phantom{\rule{0ex}{0ex}}\frac{{x}^{2}}{{2}^{2}}+\frac{{y}^{2}}{{8}^{2}}=1$

We have $b=2,a=8$ in ${b}^{2}={a}^{2}-{c}^{2}$

${c}^{2}={8}^{2}-{2}^{2}\phantom{\rule{0ex}{0ex}}{c}^{2}=60\phantom{\rule{0ex}{0ex}}c=\sqrt{60}\phantom{\rule{0ex}{0ex}}c=2\sqrt{15}$

The foci are at $(0,\pm 2\sqrt{15})$.

The vertices of the major axis of the ellipse are at $(0,8)$and $(0,-8)$.

The vertices of the minor axis of the ellipse are at $(2,0)$ and $(-2,0)$.

The graph of the function is

94% of StudySmarter users get better grades.

Sign up for free