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Question

lf x1, x2, x3 are the abscissa of the points, A1, A2, A3 respectively where the lines y=m1x,y=m2x and y=m3x meet the line 2x−y+3=0 such that m1,m2,m3 are in A.P. then x1, x2, x3 are in

A
A.P.
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B
G.P.
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C
H.P.
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D
A.G.P.
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Solution

The correct option is D H.P.
Let, y=mx is a line which meets 2xy+3=0
Subsitute y=mx in 2xy+3=0 to get
x=3m2 & y=3mm2
x1=3m12 & y1=3m1m12
x2=3m22,x3=3m32

Given, m1,m2,m3 are in A. P.
So, m12,m22,m32 are also in A.P.
1m12,1m22,1m32 are in H.P.
3m12,3m22,3m32 are also in H.P.

x1,x2,x3 are in H.P.

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