If the normal to a parabola y2=4ax at P meets the curve again in Q and if PQ and the normal at Q makes angle α and β, respectively, with the x−axis then tanα(tanα+tanβ) has the value equal to
A
0
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B
−2
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C
−12
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D
−1
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Solution
The correct option is B−2 Let the given equation of parabola is y2=4ax
Let the normal at P(at12,2at1) meets the parabola again at Q(at22,2at2).
Equation of normal at P is given by, y=−t1x+2at1+at31
Equation of normal at Q is given by, y=−t2x+2at2+at32