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Question

A straight line through (2,2) intersect the lines, y+x3=0 and yx3=0 at A and B. If OAB (where O is the origin) is an equilateral triangle, then the equation of AB is

A
x2=0
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B
y2=0
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C
xy=0
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D
x+y4=0
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Solution

The correct option is B y2=0
y=x3 has a slope 3 and is inclined at 600 to the x-axis i.e OX

and y=x3 is inclined at 600 to OX

AOY=BOY=300 since, OY is equally inclined to OA and OB, AB must be parallel to x-axis and also passes through (2,2)

Hence equation of AB(through P) is y=2

389696_258587_ans_dd410a7217ba4887b3fdc98c313f2d82.png

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