Answer

Let A(-2,8),B(-3,-5) and P(x,y). If P is equidistant from A,B and then PA =PB

Distance formula=√((x₂ - x₁)² + (y₂ - y₁)²)

PA=√((+2)² + (-8)²)

=√(x² + 4x + + y² - 16y + )

=√(x² + y² + 4x - 16y + )

PB=√((+3)² + (+5)²)

=√(x² + 6x + + y² + 10y + )

=√(x² + y² + 6x + 10y + )

Now PA=PB

=√(x² + y² + 4x - 16y + ) = √(x² + y² + 6x + 10y + )

Squaring on both sides we get

=x²+y²+4x-16y+=x²+y²+6x+10y+

=4x-16y-6x-10y=-

-2x-26y=-

x+13y= is required condition.