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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Straight Lines
Forum Index -> Analytical Geometry like the article? email it to a friend.  
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[Post New]6 Apr 2008 11:57:47 IST
    Subject: Straight Lines
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nasa_hs (25)

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If y=ax is one of the lines belongin to the family of lines representing the sides of an equilateral triangle with one vertex at the origin, then the product of the slopes of all the lines of this family is
 
a3
a(a2-3)
a(1-3a2)
a(a2-3)/1-3a2
    
[Post New]6 Apr 2008 12:07:17 IST
    Subject: Re:Straight Lines
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nidhi_nidhi (16)

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is ans z c
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[Post New]6 Apr 2008 12:18:41 IST
    Subject: Re:Straight Lines
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raulrag009 (1194)

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I think it's (D)
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[Post New]6 Apr 2008 12:38:15 IST
    Subject: Re:Straight Lines
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Conjurer (529)

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I will try:

One line is y = ax

Slope = a, let the angle be @.

The angle that the other line makes with the positive x direction can be @ + pi/3

tan(@+pi/3) = a + root(3)/1-aroot(3)

So the other line has the equation y = [a+root(3)/1-aroot(3)]x

Now using geometry,I got the slope of the third line as tan(@ -60)

= a -root3/1+aroot3

So just multiply to get answer D
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