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mun
Member of the 'S.O.S. Math' Hall of Fame
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 Posted: Thu, 5 Nov 2009 07:16:41 UTC Post subject: straight line |
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if a variable line drawn through the point of intersection of straight lines x/a+y/b=1 and x/b+y/a=1 meets the coordinate axes in A and B ,then the locus of the mid point of AB is .
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Last edited by mun on Fri, 6 Nov 2009 06:21:02 UTC; edited 1 time in total |
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robbwrr
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Location: baltimore, md
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| Posted: Thu, 5 Nov 2009 12:19:03 UTC Post subject: Re: straight line |
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| mun wrote: | | if a variable line drawn through the points of intersection of straight lines x/a+y/b=1 and x/b+y/a=1 meets the coordinate axes in A and B ,then the locus of the mid point of AB is . |
" ... points of intersection ... " ?? Distinct intersecting lines have a
single point in common. To what points do your refer? And other
than obviously not equalling zero, are there any restrictions on a
and b?? If equal the lines are not distinct; if opposite the lines are
parallel. Is this the complete statement of the original problem??
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mun
Member of the 'S.O.S. Math' Hall of Fame
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| Posted: Fri, 6 Nov 2009 06:20:07 UTC Post subject: Re: straight line |
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[quote="robbwrr"] | mun wrote: | | if a variable line drawn through the points of intersection of straight lines x/a+y/b=1 and x/b+y/a=1 meets the coordinate axes in A and B ,then the locus of the mid point of AB is . |
good morning sir(change in place of points write point)
sir this is the exact statement written in well reputated examination paper.
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Denis
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Location: Ottawa Ontario
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| Posted: Fri, 6 Nov 2009 15:11:35 UTC Post subject: Re: straight line |
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| mun wrote: | | mun wrote: | | if a variable line drawn through the points of intersection of straight lines x/a+y/b=1 and x/b+y/a=1 meets the coordinate axes in A and B ,then the locus of the mid point of AB is . |
good morning sir(change in place of points write point)
sir this is the exact statement written in well reputated examination paper. |
IT IS? What is a "variable line"?
Do you realise that x/a + y/b = 1 is same as y = (-b/a)x + b
and x/b + y/a = 1 is same as y = (-a/b)x + a ?
And that solving results in x = y?
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aswoods
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Joined: 23 Feb 2009
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Location: Adelaide, Australia
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| Posted: Fri, 6 Nov 2009 21:29:44 UTC Post subject: |
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Denis has done the first bit for you: the point of intersection will be on y=x somewhere.
Suppose that you fix a point (a,a). Draw a pair of axes, plot the point, then consider an arbitrary line passing through (a,a). Can you figure out where it passes through the axes? (Hint: draw a square with sides of a between the point (a,a) and the axes, then look at the triangles formed.) |
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