Question

If the distance of p(x,y) from A(5,1) and B(-15) are equal then prove that 3x=2y.

Answer 1

The distance from P(x, y) and A(5, 1) is, by the Distance Formula: 
√[(x - 5)^2 + (y - 1)^2]. 

The distance from P(x, y) and B(-1, 5) is: 
√[(x + 1)^2 + (y - 5)^2]. 

Since the distances are the same, equating: 
√[(x - 5)^2 + (y - 1)^2] = √[(x + 1)^2 + (y - 5)^2] 
==> (x - 5)^2 + (y - 1)^2 = (x + 1)^2 + (y - 5)^2, by squaring 
==> (x^2 - 10x + 25) + (y^2 - 2y + 1) = (x^2 + 2x + 1) + (y^2 - 10y + 25) 
==> x^2 - 10x + y^2 - 2y = x^2 + 2x + y^2 - 10y 
==> -10x - 2y = 2x - 10y 
==> -12x = -8y 
==> 3x = 2y, as required. 

I hope this helps!

Answer 2

I hope you will got this.
All the best