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If the lines px^2-qxy-y^2=0 makes the an...

If the lines `px^2-qxy-y^2=0` makes the angles `alpha` and `beta` with X-axis , then the value of `tan(alpha+beta)` is

A

`(-q)/(1+p)`

B

`(q)/(1+p)`

C

`(p)/(1+q)`

D

`(-p)/(1+q)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the lines represented by the equations `px^2-qxy-y^2=0`
be `y=m_1xand y=m_2x`
Then ,`m_1=tanalpha and m_2=tanbeta`
Also, `m_1+m_2=-qand m_1m_2=-p`
Now , `tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)=(m_1+m_2)/(1-m_1m_2)=(-q)/(1+p)`
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