00:01
So i have the equation x squared plus y squared equals 25.
00:07
And i want to find the equation of the tangent line and the normal line at the point 3 .4.
00:17
So i'm first going to find the derivative of this function.
00:21
That's going to be 2x d x d x plus 2y, d y, d x equal to 0.
00:31
So 2y, d, d, x is going to equal negative 2x.
00:38
I'm going to divide both sides by 2y.
00:43
So d, y, d, x is going to equal negative x over y.
00:49
That's going to give me my slope.
00:52
So i have negative 3 over 4.
00:56
So my tangent line is going to just be y minus 4 equals negative 3 fourths x minus 3 that's negative 3 fourths x plus 9 4th now i'm going to add 4 to both sides so that's adding 16 4ths 16 plus 9 gives me 25 over 4 now i want my normal line so my normal line is perpendicular to the tangent line.
01:40
So that means my slope is going to be a positive four -thirds.
01:45
Y minus four equals four -thirds x minus three.
01:53
That's four -thirds -x minus four.
01:58
Add four, and i have y equals four -thirds -x for the equation of the normal line...