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Question

The axes being inclined at an angle of 60o, the angle between the two straight lines y=2x+5 and 2y+x+7=0 is

A
90
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B
tan153
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C
tan132
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D
tan153
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Solution

The correct option is D tan153
Consider equation (i)
y=2x+5
Therefore, tanθ=msinω1+mcosω
=2(32)1+(2)12
=32 ...(a)
Consider equation (i)
2y=x7
Therefore, tanθ=msinω1+mcosω
=12321+1212
=13 ...(b)
Now,
M=ab1+ab
=∣ ∣ ∣ ∣52312∣ ∣ ∣ ∣
=53

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