Height and DistanceHard
Question
A variable point ′P′ is moving such that its distances from a line 
and a point (4,5,8) are equal, then vertex of the locus of P, is -
and a point (4,5,8) are equal, then vertex of the locus of P, is -Options
A.
B.(6,4,7)
C.(2,6,9)
D.
Solution
Locus of variable point ′P′ is a parabola with given line as directrix and given point as focus. Vertex is the mid point of S and foot of perpendicular ′N′.
Let N be (-1 + 3λ,2 + 4λ, 7 + 2λ)
= (5 - 3λ)î + (3 - 4λ)ĵ + (1 - 2λ)
. (3î + 4ĵ + 2
) = 0 ⇒ λ = 1
N ≡ (2,6,9)
⇒ V ≡
Let N be (-1 + 3λ,2 + 4λ, 7 + 2λ)
= (5 - 3λ)î + (3 - 4λ)ĵ + (1 - 2λ). (3î + 4ĵ + 2) = 0 ⇒ λ = 1N ≡ (2,6,9)
⇒ V ≡
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