Given,

A be the point (1, 2) and B be any point on the curve x 2 + y 2 = 16,

And the centre of the locus of the point P, which divides the line segment AB in the ratio 3 : 2 is the point

Now let the point on the circle x 2 + y 2 = 16 be 5(4 cos ,4 sin ) Now using section formula in A(1, 2) and 5(4 cos ,4 sin ) we get,

Now squaring and adding we get,

So, the centre of the locus is

Hence, by distance formula we get,

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