Question

if point (x,y) is equidistant from the point (5,1) and(-1,5) prove 3x=2y

Answer 1

Distance of (x,y) from (5,1)= √((x-5)² + (y-1)²)

Distance of (x,y) from (-1,5)= √((x+1)² + (y-5)²)

Distance of (x,y) from (5,1) = Distance of (x,y) from (-1,5)

√((x-5)² + (y-1)²) = √((x+1)² + (y-5)²)

Squaring on both sides

(x-5)² + (y-1)² = (x+1)² + (y-5)²

x²+25-10x+y²+1-2y=x²+1+2x+y²+25-10y

(because (a+b)²=a²+b²+2ab)

cancelling same terms on both sides

-10x-2y=2x-10y

-10x-2x=-10y+2y

-12x=-8y

-4(3x)=-4(2y)

3x=2y