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Question

An iron rod of length 3 units is such that its end points are always in contact with co-ordinate axes. Then locus of point of trisection of this rod contains the point

A
(1,0)
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B
(2,0)
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C
(0,1)
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D
(0,2)
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Solution

The correct option is D (0,2)

Point of trisection divides a given line in the ratio of 2:1 or 1:2,

Case 1: Let P divides AB in the ratio 1:2.
(x1,y1)=(2h3,k3)
h=3x12, k=3y1
¯¯¯¯¯¯¯¯AB=39x24+9y2=9
Locus is x24+y2=1

Case 2: Let P divides AB in the ratio 2:1.
(x1,y1)=(h3,2k3)
h=3x1, k=3y12
¯¯¯¯¯¯¯¯AB=39x2+9y24=9
Locus is x2+y24=1

x24+y2=1 passess through (2,0) and (0,1).

x2+y24=1 passess through (1,0) and (0,2).

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