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06/01/2022 12:44 pm
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Tangent and normal at P(2, -4) to parabola y2 = 8x meet directrix at A and B. Q(a, b) is such that APBQ is a square. Find 2a + b.
(a) -12
(b) -16
(c) -20
(d) -18
1 Answer
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06/01/2022 12:48 pm
Correct answer: (b) -16
Explanation:
y2 = 8x
⇒ a = 2
Tangent equation -4y = 4(x + 2)
⇒ x + y + 2 = 0
Normal: x - y + 6 = 0
Directrix x + 2 = 0
A = (-2, 0), B = (-2, -8)
Because, mid-point AB is (-2, -4)
So, Q = (-6, -4)
2a + b = -16