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# 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.

Answer :

Key points to solve the problem:

• Idea of distance formula- Distance between two points A(x_{1},y_{1}) and B(x_{2},y_{2}) is given by- AB =

How to approach: To find locus of a point we first assume the coordinate of point to be (h, k) and write a mathematical equation as per the conditions mentioned in question and finally replace (h, k) with (x, y) to get the locus of point.

Let the point whose locus is to be determined be (h,k)

Distance of (h,k) from (2,0) =

Distance of (h,k) from (1,3) =

According to question:

Squaring both sides:

⇒

⇒

Replace (h,k) with (x,y)

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

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