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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.

karthik peerlagudem , 12 Years ago

Grade

2 Answers

Prajwal kr

Last Activity: 12 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

Last Activity: 6 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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