straight lines 2

P is the point (-1,2) , a variable line through p cuts the axes in A and B . Q is a point on AB such that PA, PQ ,PB are in H.P. find the locus of Q

1 Answers

1357

Manish Shankar ·2014-03-28 04:28:30

lets assume the line to be

(x+1)/cosÎ¸=(y-2)/sinÎ¸=r

so any point on this line (-1+rcosÎ¸, 2+rsinÎ¸)

for A let it be r1, then A (-1+r₁cosÎ¸, 0)

so we have 2+r₁sinÎ¸=0

Q(-1+r₂cosÎ¸, 2+r₂sinÎ¸)=(h,k)

B(0, 2+r₃sinÎ¸) SO r₃=1/cosÎ¸

1/r₁+1/r₃=2/r₂

proceed in this way to get the answer

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