00:01
We want to find an equation for the point's equidistant from the x -axis and the point zero -zero -two.
00:11
So let's just go ahead and draw a little graph over here of what we're working with.
00:22
And so if we just call this point p x, y, z, so we'll just put it off in space here.
00:34
The point zero two call right here so that's zero zero two now what we want is we want the distance between this blue point and this green point to be the same distance to the x -axis and that point there where we don't really know what that point is without really knowing what that distance has to be but we can go ahead and call that point just a zero zero because we know the y and the z component should be zero of it so what we're going to do now is let's just find the distance of each of these so the distance between the point p and zero zero two well to find that we're going to use the distance formula which i have over here in the top right corner so p is x y z so we're just going to do x minus zero squared plus y minus zero squared plus z minus two squared square root all of this and then to find the distance between p and the x axis because remember we want this to be equidistant.
02:16
It's going to be a00.
02:21
And then we're going to do the same thing.
02:23
There's going to be a minus or x minus a plus y minus 0 squared plus z minus zero squared.
02:32
And then we square root all of this.
02:34
Now we want both of these equations here to equal each other.
02:39
Or maybe i should just do it like this.
02:41
We want those to equal.
02:43
So let's just go ahead and do the outer.
02:45
To random, set them equal.
02:47
So, for the green equation, it's going to be x squared plus y squared, and foiling out z minus 2 squared, we're going to get z squared minus 4 z plus 4, all squared rooted...