# line segment AB of length 'a' moves with its ends on the axis the locus of the point p which divides the segment in the ratio 1/2




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)

By the given ratio of 1:2 section formula:

So, 2y/3= k and x/3 = h

So y= 3k/2 and x= 3h

Now

$x^2+y^2=a^2$

Therefore

$9h^2+\frac{9k^2}{4}=a^2$

Required locus is

$9x^2+\frac{9y^2}{4}=a^2$ .

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