Answer:
The equation of ellipse centered at the origin
![\frac{x^2}{18} +\frac{y^2}{10} =1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B18%7D%20%2B%5Cfrac%7By%5E2%7D%7B10%7D%20%3D1)
Step-by-step explanation:
given the foci of ellipse (±√8,0) and c0-vertices are (0,±√10)
The foci are (-C,0) and (C ,0)
Given data (±√8,0)
the focus has x-coordinates so the focus is lie on x- axis.
The major axis also lie on x-axis
The minor axis lies on y-axis so c0-vertices are (0,±√10)
given focus C = ae = √8
Given co-vertices ( minor axis) (0,±b) = (0,±√10)
b= √10
The relation between the focus and semi major axes and semi minor axes are ![c^2=a^2-b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2-b%5E2)
![a^{2} = c^{2} +b^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%3D%20c%5E%7B2%7D%20%2Bb%5E%7B2%7D)
![a^{2} = (\sqrt{8} )^{2} +(\sqrt{10} )^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%3D%20%28%5Csqrt%7B8%7D%20%29%5E%7B2%7D%20%2B%28%5Csqrt%7B10%7D%20%29%5E%7B2%7D)
![a^{2} =18](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%3D18)
![a=\sqrt{18}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B18%7D)
The equation of ellipse formula
![\frac{x^2}{a^2} +\frac{y^2}{b^2} =1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D%20%2B%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%20%3D1)
we know that ![a=\sqrt{18} and b=\sqrt{10}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B18%7D%20and%20b%3D%5Csqrt%7B10%7D)
<u>Final answer:</u>-
<u>The equation of ellipse centered at the origin</u>
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