Question

Find the relative between a and b such that points a,b is equidistant from the points 8,3and 2,7

Answer 1

let point A(8,3) and B(2,7) be equal dis. from point C(a,b)
now
AC=AB
AC^2=AB^2
so by distance formula

${(8 - a)}^{2} + {(3 - b)}^{2} = {(2 - a)}^{2} \\ + {(7 - y)}^{2}$
64+a^2-16a+9+b^2-6b = 4+a^2-4a+49+y^2-14y
73-12a=53-8y
12a-8y-20=0
is the required relation