ParabolaHard

Question

The line 2(x - a) + cy = 0 cuts the parabola y2 = 8x at P(2t12, 4t1) and Q(2t22, 4t2). If a∈ [2,4] and c ∈ R then t1t2 belongs to -

Options

A.[-2,-1]
B.[-4,-2]
C.[-4,-3]
D.[-3,-2]

Solution

          
Line 2(x - a) + cy = 0 always passes through
(a,0) slope of PR = slope of QR
  ⇒ t1t2 = -
∵ a ∈ [2,4] ⇒ t1t2 ∈ [-2,-1]

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