Question

P(x,y) isequidistant A (5, 1) B(5,1) to prove 3x=2y ​

Answer 1

Answer:

3x = 2y

Hence proved

Since P (x, y) is equidistant from A (5, 1) and B (-1, 5), then

PA = PB

or

PA² = PB²

(5 – x)² + (1 – y)² = (– 1 – x)² + (5 – y)²

(25 + x² – 10x) + (1 + y² – 2y) = (1 + x² + 2x + 25 + y² – 10y)

26 + x² – 10x + y² – 2y = (26 + x² + 2x + y² – 10y)

12x = 8y

3x = 2y

Hence proved.

Answer 2

Answer:

Let the point P(x,y) be equidistant from the points A(5,1) and B(-1,5). then,

Let the point P(x,y) be equidistant from the points A(5,1) and B(-1,5). then,PA=PB

5,1) to prove 3x=2y

Since P (x, y) is equidistant from A (5, 1) and B (-1, 5), then PA = PB or PA2 = PB2 (5 – x)2 + (1 – y)2 = (– 1 – x)2 + (5 – y)2 (25 + x2 – 10x) + (1 + y2 – 2y) = (1 + x2 + 2x + 25 + y2 – 10y) 26 + x2 – 10x + y2 – 2y = (26 + x2 + 2x + y2 – 10y) 12x = 8y 3x =