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The equation (ay-bx)^(2)+4xy=0 has ratio...

The equation `(ay-bx)^(2)+4xy=0` has rational solutions `x`, `y` for

A

`a=(1)/(2)`,`b=2`

B

`a=4`,`b=(1)/(8)`

C

`a=1`,`b=(3)/(4)`

D

`a=2`,`b=1`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`(a,c)` `(ay-bx)^(2)+4xy=0`
`implies a^(2)y^(2)+b^(2)x^(2)+(4-2ab)xy=0`
`implies(a^(2)y)/(x)+(b^(2)x)/(y)-(2ab-a)=0`
Put `(y)/(x)=t`
`impliesa^(2)t^(2)-(2ab-4)t+b^(2)=0`
`D=(2ab-4)^(2)-4a^(2)b^(2)`
`=4(4-4ab)=16(1-ab)` must be a perfect square.
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