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

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
let the equation of exlipse be
$\frac{\left(x-\alpha {\right)}^{2}\right)}{{a}^{2}}+\frac{\left(y-\beta {\right)}^{2}}{{b}^{2}}=1$
the coordinate of vortex, focus and center are $\left(\alpha +a,\beta \right),\left(\alpha +ae,\beta \right)$ and $\left(\alpha ,\beta \right)$
Given equations
center =(5,-5)
vertex =(8,-5)
focus =(7,-5)
So,
$\alpha +a=8⇒a=8-5=3\phantom{\rule{0ex}{0ex}}\beta =-5\phantom{\rule{0ex}{0ex}}\alpha =5\phantom{\rule{0ex}{0ex}}\alpha +ae=7⇒b=\sqrt{5}$
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