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Analytical Geometry

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24 Oct 2007 13:17:11 IST

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1)ABC is a variable triangle with a fixed centroid(5,5) Side BC =13 and B and C

move on X & Y axis resp. Find the equation of the locus of the vertex A

2)A line AB of length 2l moves with the end A always on X axis and end B on the line y=6xFind the equation of locus of the middle point of AB

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Nadeem

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Joined: 25 Aug 2007

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24 Oct 2007 14:32:37 IST

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let the points B and C be ( a,0) and (0,b).
Let the point A be (h,k).

a^2 + b^2 = 13^2

( a+ h ) /3 = 5 , ( k+b) / 3 =5

a=15-h and b= 15-k

therefore ( 15-h) ^2 + ( 15-k)^2 = 13^2

or ( h-15 ) ^2 + ( k-15)^2 = 13^2

( x-15 ) ^2 + ( y-15)^2 = 13^2

So the locus of A is a circle is a circle with centre ( 15,15) and radius 13

Bipin Dubey

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Joined: 23 Jan 2007

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24 Oct 2007 16:39:38 IST

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Good work Nadeemoidu.

Locate two variable points B,Con axes and apply the BC = 13.

Let A be (h,k)

Now find the centroid and match it with the given centroid.

Now you have 3 equations, use them to eliminate a and b to get the required locus of (h,k).

rashmi varma

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24 Oct 2007 17:11:33 IST

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point A be (a.0) and pt B (b,6b)

mid point of AB = (h,k)

a+b/2 =h--------(1) ; 3b=k-------(2)

from (1) nd (2) 3a+k=6h or, a=6h-k/3

length of AB:- (2l)^2 = (6b)^2 +(a-b)^2

= (2k)^2 + [(6h-k-k)/3]^2

open the brackets replace h,k by x,y

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