Question

Find the equation of the locus of the point which is equidistant from the points $(-3,7)and(4,2).$

Answer 1

Let the locus be $P(x,y)$

Let $A=(-3,7),B=(4,2)$

As per the given conditions

$PA=PB$

$P{A}^2=P{B}^2$

$(x+3{)}^2+(y-7{)}^2=(x-4{)}^2+(y-2{)}^2$

$6x+9-14y+49=-8x+16-4y+4⟹14x-10y+38=0⟹7x-5y+19=0$