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 `(alp

Question

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 `(alp

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)`.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

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)`

5 views Answered 2023-02-05 15:29