00:01
All right, problem is 70.
00:04
Find the equation of a line that's tangent to x minus 1 squared plus y minus 1 square equals 25 at 0 .4 negative 3.
00:16
All right, so this is going to pull in a lot of stuff from your previous math classes here.
00:21
First off, you have to recognize that this is a circle.
00:25
And it's going to be a circle with center at 1 -1.
00:34
The opposite of this and the opposite of that.
00:38
And the radius equals five.
00:42
So 1 -1.
00:45
There's the center and the radius is five.
00:47
So that means i'm going to go five in each direction, right, left, up and down, and then try to connect them up.
00:53
So right, five would be to six, up five would be the six, left five would be the four.
01:02
Oh, five be the four.
01:03
Down five would be the four okay also know that it goes through this point right here i could verify that if i didn't trust the book or something but i'm trusting that they're giving us that because it's on the circle okay so this is going to be kind of hard to draw so bear with me here so this circle does something like this oh well you get the idea right and it goes through this point right here now here's another thing you got to pull out of your little pocket of knowledge and that is that the tangent line to a circle is perpendicular to the to the radius at the point of tangency okay so this is the point where it's tangent which means that this is this line here this radius is perpendicular to this line right here.
02:10
So that's the key to finding this equation.
02:12
We already know a point that the line goes through, but we need to have a slope.
02:18
And so we know the slope is going to be the opposite reciprocal of the slope here...