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Question

The equation x25xy+py2+3x8y+2=0 represents a pair of straight lines. If θ is the acute angle between them, then sinθ equals

A
150
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B
17
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C
15
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D
110
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Solution

The correct option is A 150
For pair of straight lines,
Δ=0
(1)(p)(2)+2(4)(32)(52)1(4)2p(32)22(52)2=0
2p+3016(94)p(252)=0
p=6

tanθ=2h2ab|a+b| =22546|1+6|=17sinθ=150

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