If the lines represented by the equation ax 2- bxy - y 2-0 make angles - and - with the x - axis- then tan -A- a-1-bB- None of theseC- b-1-aD- -b-1-a

The correct option is D Here the equation is ax^2 bxy y^2 = 0 and given that m_1 = tanα and nbsp;m_2 nbsp;= tanβ and we know that nbsp; m_1 + m_2 = ...

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Byju's Answer

Standard XII

Mathematics

Pair of Lines Passing Though Origin

If the lines ...

Question

If the lines represented by the equation $a x^{2} - b x y - y^{2} = 0$ make angles $α$ and $β$ with the x - axis, then $tan (α + β)$ =

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None of these

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Solution

The correct option is B

Here the equation is $a x^{2} - b x y - y^{2} = 0$ and given that $m_{1} = t a n α$ and $m_{2} = t a n β$ and we know that

$m_{1} + m_{2} = \frac{b}{- 1} = t a n α + t a n β$

and $m_{1} m_{2} = \frac{a}{- 1} = t a n α t a n β$

$t a n (α + β) = \frac{t a n α + t a n β}{1 - t a n α t a n β} = \frac{- b}{1 - (- a)} = \frac{- b}{(1 + a)}$ .

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