Find the equation of the locus of a point which moves such that the ratio of its distance from (2, 0) and (1, 3) is 5: 4.

Solution:

Let P (h, k) represent any point on the locus

And let the coordinates of A and B be (2, 0) and (1, 3) respectively.

So then,

PA/ BP = 5/4

Thus, we can say: PA² = BP² = 25/16