The eccentricity of the ellipse `(x -3)^2 + (y-4)^2=y^2/9`

Options

A. `(sqrt(3))/(2)`
B. `(1)/(3)`
C. `(1)/(3sqrt(2))`
D. `(1)/(sqrt(3))`

Answer

B

Explanation

`9(x-3)^(2) +9(y-4)^(2) =y^(2)`
`rArr 9(x-3)^(2) + 8y^(2) - 72y +144 =0`
`rArr 9 (x-3)^(2) + 8(y^(2) -9y) +144 =0`
`rArr 9 (x-3)^(2) + 8 [(y-(9)/(2))^(2)-(81)/(4)] +144 =0`
`rArr 9(x-3)^(2) + 8 (y-(9)/(2))^(2) = 162- 144 = 18`
`rArr(9(x-3)^(2))/(18) +(8(y-(9)/(2)))/(18) =1`
`rArr ((x-3)^(2))/(2) + ((y-(9)/(2)))/(9//4) =1`
`rArr e^(2) = 1 -(2xx 4)/(9) = (1)/(9) rArr e = (1)/(3)`