A rod `A B` of length `15c m` rests in between two coordinate axes in such a way that the end point `A` lies on `x-`axis and end point `B` lies on `y`-axis . A point is taken on the rod in such a way that `A P=6c m` . Show that the locus of `P` is an ellipse.

Explanation

Let AB be rod & P(x,y) be any point on rod such that AP=6 cm,AB=15 cm & BP=9 cm

Let A(a,0) & B(0,b) be the co-ordinates of point A and B
P(x,y) divides AB in ratio 6:9


using section formula

`x=(2(0)+3(a))/5​ & `

`y=((2b)+3(0))/5​`

`x=(3a)/5​ & y=(2b)/5​`

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