[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex] is the equation of the ellipse.
The equation of an ellipse is given by
[tex]\rm \dfrac{ (x-h)^2 }{a^2} + \dfrac{ (y-k)^2}{b^2} = 1[/tex]
here
(h,k) is the center
c = is the distance between center to focus
c = [tex]\rm \sqrt{a ^2 - b^2}[/tex]
as the a = 10 , component length
and c = 8
8 = [tex]\rm \sqrt{10 ^2 - b^2}[/tex]
8² = 10² -b²
b² = 36
b = 6
h = 0 ,k = 0
Substituting the values given
[tex]\rm \dfrac{ (x-0)^2 }{10^2} + \dfrac{ (y-0)^2}{6^2} = 1[/tex]
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex]
Therefore the equation of the ellipse has been determined.
To know more about Ellipse
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