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
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1 Answers
1357lets assume the line to be
(x+1)/cosθ=(y-2)/sinθ=r
so any point on this line (-1+rcosθ, 2+rsinθ)
for A let it be r1, then A (-1+r1cosθ, 0)
so we have 2+r1sinθ=0
Q(-1+r2cosθ, 2+r2sinθ)=(h,k)
B(0, 2+r3sinθ) SO r3=1/cosθ
1/r1+1/r3=2/r2
proceed in this way to get the answer
