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the line joining (5,0) to (10 cos θ ,10sin θ ) is dividedinternally in the ratio 2:3 at P.If varies,then the locus of P is.

the line joining (5,0) to (10 cosθ ,10sinθ ) is dividedinternally in the ratio 2:3 at P.If varies,then the locus of P is.

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2 Answers

Prajwal kr
49 Points
11 years ago

I give you the idea:

Let any point on locus be (h,k)

Apply section formula. Get a relation such that you get 

cosθ= some value in terms of h........................................(1)

sinθ= some value in terms of k....................................(2)

 

Square the equaltions and add them. 

sinθ and 

cosθ are elimintated. This will be the locus.

 
Chakshu Shah
33 Points
5 years ago
(h,k) =[2(10\large \cos \theta)+3(5)/5 , 2(10\large \sin \theta)+3(0)/5]
        =[4\large cos \theta+3 , 4\large \sin \theta]
\large \therefore h = 4\large cos \theta+3 and also k= 4\large \sin \theta
So, \large cos \theta= h-3/4......................(1)
       \large \sin \theta=k/4.........................(2)
Squaring and adding both the equantions,
\large \therefore \large \cos ^{2}\theta +\sin ^{2}\theta=\large h^{2}+9-6h +k^{2}\large /16
\large \therefore \large 16=h^{2}+ k^{2}-6h+9
\large \therefore h^{2}+k^{2}-6h-7=0
If \large \theta varies then locus of P is a circle
 

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