The lie x−b+λy=0 cuts the parabola y2=4ax at P(t1) and Q(t2). If b∈[2a,4a] and λ∈R, then the value(s) [t1t2] is/are
(where [.] repreasents the greatest integer function and t1,t2 are parametic points)
A
−5
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B
−4
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C
−3
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D
−2
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Solution
The correct option is D−2 Given P(t1)≡(at21,2at1) and Q(t2)≡(at22,2at2)
Now line x−b+λy=0 always passes through (b,0)
Slope of PR= Slope of RQ ⇒2at1at21−b=2at2at22−b⇒t1t2=−ba
Now from b∈[2a,4a] t1t2∈[−4,−2]