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Analytical Geometry

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22 Oct 2007 18:11:33 IST

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question from co-ordinate geometry?

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A STRAIGHT LINE MOVES SO THAT THE SUM OF THE RECIPROCALS OF IT'S INTERCEPTS ON THE AXES OF COORDINATE IS CONSTANT. SHOW THAT IT WILL ALWAYS PASS THROUGH A FIXED POINT?

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Bipin Dubey

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Joined: 23 Jan 2007

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22 Oct 2007 18:22:27 IST

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Let the variable line be x/a + y/b = 1

Length of its intercepts are a and b.

Sum of their reciprocals = 1/a + 1/b is a constant, let this constant be c.

1/a + 1/b = c

Now divide both sides by c.

(1/c)/a + (1/c)/b = 1

This equation shows that the variable line passes through (1/c,1/c) for variables values of a and b.

Karthik M

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Joined: 1 May 2007

Posts: 2830

22 Oct 2007 21:30:25 IST

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i dont get what u have done... how did u get that 1/c/a step?

karthik vadlamani

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Joined: 3 Nov 2007

Posts: 91

8 Nov 2007 19:53:04 IST

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easy yaar. 1/a+1/b=k(let),a,b are intercepts
then,1/k/a+1/k/b=1.compare it with x/a+y/b=1
hence,(x,y)=(1/k,1/k) which is a fixed point through which the line passes.
please rate me if i was correct.

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