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For the eliiipse 24x^(2)+9y^(2)-120x-90y...

For the eliiipse `24x^(2)+9y^(2)-120x-90y+225=0`, the eccentricity is equal to

A

`(2)/(5)`

B

`(3)/(5)`

C

`sqrt((15)/(24))`

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given equation can be rewritten as
`24(x^(2)-5x+(25)/(4))+9(y^(2)-10y+25)`
`+225-150-225=0`
`implies((x-(5)/(2))^(2))/((150)/(24))+((y-5)^(2))/((150)/(9))=1`
`therefore esqrt(1-(a^(2))/(b^(2)))=sqrt(1-(9)/(24))=sqrt((15)/(24))`.
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