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# Let L1=0, L2=0 and L3=0 are three given lines .A variable line is drawn through the origin to cut the lines at A, B, and C, respectively. If P is a point on variable line in such a way that,7/OP=1/OA+2/OB+4/OC , then find the locus of P.

## 1 Answers

10 years ago

let the three lines be  y=m1x +c1, y=m2x +c2 and y=m3x +c3. Let variable line be y=mx. A=(c1/(m-m1),mc1/(m-m1)),

B= (c2/(m-m2),mc2/(m-m3)), and C=(c3/(m-m3),mc3/(m-m3)),. let P=(x,y)=(x,mx)

OP=√(x2(1+m2)), 1/OA= (m-m1)/c1(√(1+m2)), 2/OB= 2(m-m2)/c2(√(1+m2)) and 4/OC = 4(m-m3)/c3(√(1+m2))

Therefore,P is given by y(1/c1 +2/c2 + 4/c3) = 7 + x(m1/c1 +2m2/c2  +4m3/c3

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