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
