Amina Richards
2022-10-21
Answered

Use the given information to find the equation for the ellipse. Center at (5, −5), vertex at (8, −5), focus at (7, −5)

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Remington Wells

Answered 2022-10-22
Author has **13** answers

let the equation of exlipse be

$$\frac{(x-\alpha {)}^{2})}{{a}^{2}}+\frac{(y-\beta {)}^{2}}{{b}^{2}}=1$$

the coordinate of vortex, focus and center are $$(\alpha +a,\beta ),(\alpha +ae,\beta )$$ and $$(\alpha ,\beta )$$

Given equations

center =(5,-5)

vertex =(8,-5)

focus =(7,-5)

So,

$$\alpha +a=8\Rightarrow a=8-5=3\phantom{\rule{0ex}{0ex}}\beta =-5\phantom{\rule{0ex}{0ex}}\alpha =5\phantom{\rule{0ex}{0ex}}\alpha +ae=7\Rightarrow b=\sqrt{5}$$

$$\frac{(x-\alpha {)}^{2})}{{a}^{2}}+\frac{(y-\beta {)}^{2}}{{b}^{2}}=1$$

the coordinate of vortex, focus and center are $$(\alpha +a,\beta ),(\alpha +ae,\beta )$$ and $$(\alpha ,\beta )$$

Given equations

center =(5,-5)

vertex =(8,-5)

focus =(7,-5)

So,

$$\alpha +a=8\Rightarrow a=8-5=3\phantom{\rule{0ex}{0ex}}\beta =-5\phantom{\rule{0ex}{0ex}}\alpha =5\phantom{\rule{0ex}{0ex}}\alpha +ae=7\Rightarrow b=\sqrt{5}$$

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