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Question

If x22hxy+y2=0 represents the equation of pair of straight lines both of which make an angle θ with the straight lines x+y=2, then

A
tanθ=h1h+1
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B
cos2θ=h
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C
cotθ=h1h+1
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D
cosθ=h+12h
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Solution

The correct option is C cotθ=h1h+1
y=m1x and y=m2x
from x22hxy+y2=0
m1+m2=2h m1m2=1

m1+11m1=tanθ=m2+11m2

m1=tanθ1tanθ+1; m2=tanθ+1tanθ1

m1+m2=2h=(tanθ1)2+(tanθ+1)2tan2θ1

sec2θ2tanθ+sec2θ+2tanθtan2θ1

2h=2cos2θ

2h=2sec2θ
h=sec2θ
1h=cos2θ=2cos2θ1
cosθ=h12h

tanθ=h+1h1

cotθ=h1h+1

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