If the component lines whose combined equation is `px^(2)-qxy-y^(2)=0` make the angles `alphaand beta ` with x-axis , then find the value of tan `(alpha+beta)`.

Explanation

Given equation of pair of straight lines is :
`px^(2)-qxy-y^(2)=0` (1)
Let the component lines be `y=m_(1)xandy=m_(2)x`.
`:. m_(1)=tanalphaandm_(2)=tanbeta` (Given)
Also , `m_(1)+m_(2)=-qand m_(1)m_(2)=-p`
`:.tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)`
`=(m_(1)+m_(2))/(1-m_(1)m_(2))=(-q)/(1+p)`