A line passes through a fixed point R intersecting a fixed line at P. A point Q on RP such that 
is constant. Then show that locus of Q is a straight line
Text Solution
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Let a fixed point R( α α , β β ) and fixed line is ax + by + c = 0
Equation of line RP is 
Coordinate of P( α α + rcos θ θ , β β + rsin θ θ ). It lies on line
ax + by + c = 0
…(i)
Let coordinate of Q(h, k) be
h = α α + r 1 cos θ θ and k = β β + r 1 sin θ θ
Given that 
(constant)
⇒ ⇒ 
From equation (i), 
Hence locus of Q is
.
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