The equation of the ellipse with foci at (0 ±10) and vertices at (0 ±11) is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
How to determine the ellipse equation?
We have:
Vertices = (0, ± 11),
Foci = (0, ± 10)
The vertices and the foci are represented as:
Foci = (0, ± a)
Vertices = (0, ± c)
So, we have:
a = 10
c = 11
The equation of b is calculated using:
b² = c²- a²
So, we have:
b² = 11²- 10²
Evaluate
b² = 21
The equation of the ellipse is then represented as:
[tex]\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]
This gives
[tex]\frac{x^2}{21} + \frac{y^2}{10^2} = 1[/tex]
[tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
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