Math miscellaneousHard
Question
Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is
Options
A.y2 - 4x + 2 = 0
B.y2 + 4x + 2 = 0
C.y2 + 4y + 2 = 0
D.y2 - 4y + 2 = 0
Solution
P = (1, 0)
Q = (h, k) such that k2 = 8h
Let(α, β) be the midpoint of PQ
α =
, β = 
2α - 1 = h 2β = k.
(2β)2 = 8 (2α - 1) ⇒ β2 = 4α - 2
⇒ y2 - 4x + 2 = 0.
Q = (h, k) such that k2 = 8h
Let(α, β) be the midpoint of PQ
α =
, β = 2α - 1 = h 2β = k.
(2β)2 = 8 (2α - 1) ⇒ β2 = 4α - 2
⇒ y2 - 4x + 2 = 0.
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