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A straight line segment AB of length a units moves with its ends one the axis. The locus of the point P which divides ther segment in the ratio 1:2 is

A straight line segment AB of length units moves with its ends one the axis. The locus of the point P which divides ther segment in the ratio 1:2 is

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
Take P (h,k)
Take end points on x and y axis as A(0,n) and B(m, 0)
Now AB=a
So n^2 + m^2 = a^2
Now P divides AB in the ratio 1:2
So h = \frac{1*m + 2*0}{2+1}….….…...(1)

similarily k = 2n/3….…....(2)

Now put the value of n and m in n^2 + m^2 = a^2 from eq 1 and 2


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