Find the standard form of the equation of the ellipse with v

Find the standard form of the equation of the ellipse with vertices (9,0) and (-9,0) and eccentricity e=2/3

Solution

vertices ( 9 , 0 ) ( -9 , 0 )

e = 2/3

length of major axis 2a = 18

a = 9

eccentricity of ellipse = c/a = c / 9

2/3 = c/9

c = 6

b^2 = a^2 - c^2

b^2 = 81 - 36 = 45

therefore equation of ellipse is

(x^2 / 81) + (y^2 / 45) = 1

Find the standard form of the equation of the ellipse with vertices (9,0) and (-9,0) and eccentricity e=2/3Solutionvertices ( 9 , 0 ) ( -9 , 0 ) e = 2/3 length

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