Questions
The locus of a point which divides the line joining and internally in the ratio for all , is
a
straight line
b
circle
c
pair of straight lines
d
parabola
detailed solution
Correct option is B
Let the coordinates of the point P which divides the line joining (1, 0) and (2cosθ,2sinθ) in the ratio 2 :3 be (h, k). Then, h=4cosθ+35 and k=4sinθ5⇒ cosθ=5h−34 and sinθ=5k4⇒ 5h−342+5k42=1⇒ (5h−3)2+(5k)2=16Hence, the locus of (h, k) is(5x−3)2+(5y)2=16, which is a circle.Talk to our academic expert!
Similar Questions
A line L cuts the sides AB, BC of ABC in the ratio 2 : 5, 7 : 4 respectively. Then the line L cuts CA in the ratio
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