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Question

The slope of a line is twice the slope of the other line. If the tangent of the angle between them is 13, then the slope of the lines are

A
1 and 2
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B
12 and 1
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C
1 and 2
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D
12 and 1
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Solution

The correct option is D 12 and 1
Let m1,m be the slopes of the two given lines such that m1=2m
Let θ be the angle between them, so
tanθ=m2m11+m1m2
According to given conditions, we get
13=m2m1+(2m)m13=m1+2m2m1+2m2=±13

Case 1: m1+2m2=13
2m2+3m+1=0(m+1)(2m+1)=0m=1 or m=12m1=2 or m1=1

Case 2: m1+2m2=13
2m23m+1=0(m1)(2m1)=0m=1 or m=12m1=2 or m1=1

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