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

On the first, it is a line perpendiular to the line connecting the two ponts, which intersects the half way pont (0,-1.5).

On the last, would it be an eliplse?

On the second, look for a conic.

How do you get the equations of the last two?

Pick a point (x,y).
write the distance equations to the two given points.
for 2, set twice one distance equal to the distance of the other, then maniplate the equation into standard form for x and y.
for 3, add the distances, set them equal to 12.