Question

1. Find the equation of the set of all points P(x,y) that is equidistant from (-3,0) and (3,-5).

2. Find the equation of the set of all points P(x,y) that is twice as far from (-8,8) as from (-2,2).

3. Find the equation of the set of all points P(x,y) such that the sum of the distance from (-4,0) and (4,0) is equal to 12.

Answer 1

1. (-3,0), (x,y), (3,-5).
(3-(-3) = 2(x-(-3), 6 = 2x+6, X = 0.

(-5-0) = 2(y-0), -5 = 2y, Y = -2.5.

(-3,0), (0,-2.5), (3,-5).
m = (-2.5-0)/(0-(-3)) = -5/6.

Y = mx + b, -5x/6 + b = 0, -5*(-3)/6 + b = 0, b = -5/2 = -2.5.
Eq: Y = (-5/6)x - 5/2.

Answer 2

2. (-8,8), (x,y), (2,2).

x-(-8) = 2(-2-x), x+8 = -4-2x, X = -4.

y-8 = 2(2-y), Y = 4.

(-8,8), (-4,4), (-2,2).

m = (4-8)/(4-(-8)) = -1.

Y = mx+b = 8, -1*(-8)+b = 8, b = 0. Eq: Y = -x.