Question

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

Answer 1

Answer:

x² + y² + 6x - 30 y + 34 = 0

Step-by-step explanation:

let A = (2,0)

    B = (1,3)

let P(h,k) be a point such that PA/PB = 5/4

 Distance between two points = √(x₂ - x₁)² + (y₂ - y₁)²

                                  PA / PB =5/4

                                            4PA      = 5PB

                      4[ (h-2)² + (k-0)² ]       = 5 [ ( h-1)² + ( k-3)² ]

                   4[ h² - 4h + 4 + k² ]       = 5 [ h² -2h + 1 + k² - 6k +9]

                        4h² -16h + 16 + 4k²  = 5h² - 10h +5 + 5k² - 30k + 45

                           h ² + k² + 34 + 6h - 30k =0

Substituting h and k with x and y,

                           x² + y² + 6x -30y +34 = 0

The locus of thw points which moves such that the ratio of its distances from (2,0) and (1,3) is 5 : 4 is

         x² + y² + 6x - 30 y + 34 = 0