Conic Sections Question 203
Question: The line joining (5, 0) to is divided internally in the ratio 2 : 3 at P. If $ \theta $ varies, then the locus of P is
Options:
A) A pair of straight lines
B) A circle
C) A straight line
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let $ P(x,y) $ be the point dividing the join of A and B in the ratio 2 : 3 internally, then $ x=\frac{20\cos \theta +15}{5}=4\cos \theta +3 $
$ \Rightarrow \cos \theta =\frac{x-3}{4} $
…… (i) $ y=\frac{20\sin \theta +0}{5}=4\sin \theta \Rightarrow \sin \theta =\frac{y}{4} $ - (ii) Squaring and adding (i) and (ii), we get the required locus $ {{(x-3)}^{2}}+y^{2}=16, $ which is a circle.
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