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An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
Which equation represents this ellipse?

Sagot :

[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex] is the equation of the ellipse.

What is the equation of an 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

https://brainly.com/question/14281133

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