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Question

If (ax2+bx+c)y+ax2+bx+c=0, then the condition that x may be rational function of y is


Solution

The correct option is B
The given equation can be written as
(ay+a)x2+(by+b)x+(cy+c)=0
The condition that x may be rational function of y is,
(by+b)24(ay+a)(cy+c) is a perfect square that is,
(b24ac)y2+(2bb4ac4ac)y+b24ac is a perfect square
D=0 that is,
4(bb2ac2ac)24(b24ac)(b24ac)=0
or    (ac+ac)4aacc=abbc+abbcabbcacb2acb2
or   (acac)2=(abab)(bcbc)

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