Question

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

Answer 1

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

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

Required locus is

$9 {x}^{2} + \frac{ {9y}^{2} }{4} = {a}^{2}$