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If $θ$ is acute angle between two lines $x^{2} + 6 xy + y^{2} = 0$ then the value of $\sqrt{2} sinθ + cosθ$ is

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a

−35

b

35

c

-53

d

53

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detailed solution

Correct option is D

If θ is acute angle between pair of lines represented by the equation ax2+2hxy+by2=0 then cosθ=a+b(a−b)2+(2h)2For the equation x2+6xy+y2=0,a=1,h=3,b=1Hence, cosθ=26=13 Use the right triangle for sinθ=223Hence, 2sinθ+cosθ=2223+13=43+13=53Therefore, 2sinθ+cosθ=53

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