The square of the differences of the slopes of the lines represented by the equation x2(sec2θ−sin2θ)−2xytanθ+y2sin2θ=0 is
A
1
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B
2
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C
4
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D
8
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Solution
The correct option is C4 Divide the complete equation by x2 which results in a quadratic with slopes of the lines as the roots.Let m1 , m2 be the roots of the quadratic. Sum of the roots m1+m2=2tanθsin2θ=4sin2θ
Product of the roots m1m2=sec2θ−sin2θsin2θ=4sin22θ−1