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Question

If θ is the angle between the lines represented by x23xy+λy2+3x5y+2=0, where λ is a real number, then cosec2θ equals :

A
9
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B
3
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C
10
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D
100
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Solution

The correct option is A 9
Solution - The guren equation of pain of lines is x23xy+λy2+3x5y+2=0 Standard form is given by- ax2+by2+2hxy+2gx+2fy+c=0 for pair of lines



∣ ∣ahghbfgfc∣ ∣=0


∣ ∣ ∣13/23/23/2λ5/23/25/22∣ ∣ ∣=0


on solving we get 1(2λ254)+32(3+154)+32(1543λ2)=02λ25492+458+45894λ=0λ=2


Now, 2n2aba+b=∣ ∣ ∣2×9423∣ ∣ ∣=13tanθ=+cot2θcosec2θ=1+1tan2θ



cosec2θ=1+9cosec2θ=10 Hence, (c) is the correct option.

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