00:01
In this point, we consider the sphere, so let's write out sphere, whose equation is given by x minus 4 squared plus y minus 3 squared plus z minus 5 squared equals to 25.
00:20
So first, where does the sphere intersect the yz plane? so in each of these, we want to decide the sphere intersect each of the following planes at zero points, at one point, or at two points in a line or in a circle.
00:36
Those are the options that were given.
00:38
So the yz plane, so the first part, let's call it a1, the yz plane, y, z plane, x is equal to zero.
00:53
So the equation of the sphere becomes negative four squared, which is 60.
00:58
Plus y minus 3 squared plus z minus 5 squared equals to 25 that means that y minus 3 squared plus z minus 5 squared is equal to 25 minus 16 is 9th and this is the equation of the circle so pretty much the sphere intersects the y z plane and it forms the circle the second part a 2 for this one, what about the xxy plane? so the xy plane implies that z is equal to zero.
01:37
So the equation of this here becomes x minus four squared plus y minus three squared plus 25 equals to 25.
01:49
So this one just gives us a point, right? because we get x minus four squared plus y minus three squared equals to zero.
01:57
That means that we get a single point.
01:59
We get the point literally 4 .3 so that's pretty much the answer that these would be the intersection would be just a point what about 8 3 so that was a 2 so 8 3 what about the x z plane so the xz plane implies that we're referring to the plane where y is equal to 0 so we're going to have x minus 4 squared and if y is equal to 0 then pretty much we get plus 9 plus z minus 5 squared equals to 25.
02:39
This will imply that we get x minus 4 squared plus z minus 5 squared equals to 16th.
02:49
And once again, we get a circle.
02:51
So let's write this out as a circle...