MATHEMATICS If \\theta is acute angle between the pair of lines x^{2}-7 x y+12 y^{2}=0 then \frac{2 \cos \\theta+3 \sin \\theta}{4 \sin \\theta+5 \cos \\theta}=?

NIMCET 2021 Question Paper with solutions

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MATHEMATICS

\θ

is acute angle between the pair of lines

x^{2}-7 x y+12 y^{2}=0

then

{2 \cos \θ+3 \sin \θ}/{4 \sin \θ+5 \cos \θ}=?

Solution:

\tan \θ={2 \√{h^{2}-a b}}/{a+b}

\tan \θ={2 \√{{49}/{4}-12}}{1+12}

\tan \θ-{1}/{13}

{2 \cos \θ+3 \sin \θ}/{4 \sin \θ+5 \cos \θ}

Divide numerator and denominator both by

\cos \θ

{2+3 \tan \θ}/{4 \tan \θ+5}={2+{3}/{13}}/{{4}/{13}-5}={29}/{69}

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