How do you write the equation of an ellipse with vertices at (-5,1) and (-1,1) and co-vertices at (-3,2) and (-3,0)?

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Answer 1 · 2016-08-06T15:18:38

$\frac{{(x + 3)}^{2}}{4} + \frac{{(y - 1)}^{2}}{1} = 1$ $(x+3)^2/4 +(y-1)^2/1=1$

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Center (h,k) lies on the x-axis .

so midpoint of vertices is the center.

$(h, k) = (\frac{- 5 + (- 1)}{2}, \frac{1 + 1}{2}) = (- 3, 1)$ $(h,k) =((-5+(-1))/2,(1+1)/2)=(-3,1)$

a=length of semi-major axis $a = 2$ $a=2$
b=length of semi-minor axis $b = 1$ $b =1$

Equation of ellipse:

$\frac{x - h}{a^{2}} + \frac{y - k}{b^{2}} = 1$ $(x-h)/a^2+(y-k)/b^2=1$

Plug the values of a,b and (h,k)

$\frac{{(x + 3)}^{2}}{4} + \frac{{(y - 1)}^{2}}{1} = 1$ $(x+3)^2/4 +(y-1)^2/1=1$