Can someone explain this question to me?

[-Whiplash-]

Hey, I've been doing this pre-calculus assignment and I ran into this Question:

"Find the equation of the set of all points (x,y) such that the absolute value of the difference between their distance to (-3,0) and to (3,0) is 4."

What do they mean? I'm certain I can do it but I have no idea what they're asking.

 

[HallsofIvy]

Hey, I've been doing this pre-calculus assignment and I ran into this Question:

"Find the equation of the set of all points (x,y) such that the absolute value of the difference between their distance to (-3,0) and to (3,0) is 4."

What do they mean? I'm certain I can do it but I have no idea what they're asking.

They mean: Calculate the distance from (x,y) to (-3, 0). That is \(\displaystyle \sqrt{(x+ 3)^2+ y^2}\). Calculate the distance from (x, y) to (3,0). That is \(\displaystyle \sqrt{(x- 3)^2+ y^2}\). Subtract the first from the second and take the absolute value, \(\displaystyle \left|\sqrt{(x+ 3)^2+ y^2}-\sqrt{(x- 3)^2+ y^2}\right|\)

Set that equal to 4 and simplify it. You can get rid of the absolute values by squaring both sides: \(\displaystyle |x|^2= x^2\).