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Find the set of those value(s) of alpha ...

Find the set of those value(s) of `alpha` for which `(7-(5alpha)/4,alpha)` lies inside the ellipse `x^2/25+y^2/16=1`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`(7-(5)/(4)alpha, alpha)` lies inside the ellipse `(x^(2))/(25) + (y^(2))/(16) =1`
`rArr ((7-(5)/(4)alpha)^(2))/(25)+(alpha^(2))/(16)-1 lt 0`
`rArr ((28-5 alpha)^(2))/(400) + (alpha^(2))/(16) -1 lt 0`
`rArr (28 - 5 alpha)^(2) + 25 alpha^(2) - 400 lt 0`
`rArr 50 alpha^(2) - 140 alpha - 192 lt 0`
`rArr (5 alpha -12) (5 alpha -16) lt 0`
`rArr (12)/(5) lt alpha lt (16)/(5)`
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