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A straight line segment AB of length 'a' moves with its ends n the coordinate axes.The locus of the point P which divides the segment AB in ratio 1:2 is

A straight line segment AB of length 'a' moves with its ends n the coordinate axes.The locus of the point P which divides the segment AB in ratio 1:2  is

Grade:12th pass

3 Answers

Arun
25750 Points
5 years ago
Dear student
 
….….…...(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 2h = \frac{1*m + 2*0}{2+1} Now P divides AB in the ratio 1:2 So n^2 + m^2 = a^2Take P (h,k) Take end points on x and y axis as A(0,n) and B(m, 0) Now AB=a So 
Arun
25750 Points
5 years ago
Dear student
 
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 =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
Rajat
213 Points
5 years ago
Let the co-ordinate of the point be (h,k)
Let the co-ordinate of the point of intersection with the Axes be ( x,0) and (0,y)
So, 2y/3= k and x/3 = h (due to the given ratio of 1:2 section formula)
So y= 3k/2 and x= 3h
Now x^2+y^2= a^2 
Therefore 9h^2+9k^2/4= a^2
Required locus is 9x^2 + 9y^2/4= a^2
 

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