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Question

If the line px2-qxy-y2=0 makes the angles α and β with x axis, then the value of tanα+β is:


A

-q1+p

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B

q1+p

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C

-q1-p

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D

None of these

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Solution

The correct option is A

-q1+p


Explanation for the correct option:

Pair of straight line:

The equation of the line is given as px2-qxy-y2=0,

It is given that α and β are the angles with x axis.

So let, slope m1=tanα and m2=tanβ

We know that if a pair of lines are represented by a homogeneous equation ax2+2hxy+by2=0 then,

sum of slopes m1+m2=-2hb and product of slopes m1m2=ab

Here, a=p,b=-1,h=-q2

Now we know that, m1+m2=-2hb

tanα+tanβ=-2×-q2-1tanα+tanβ=-q

Also, m1m2=ab, so,

tanα·tanβ=p-1tanα·tanβ=-p

Thus, we can evaluate tanα+β,

tan(α+β)=tanα+tanβ1-tanα·tanβ=-q1+p

Therefore, option (A) is the correct answer.


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