00:01
Here, we're giving an equation that 4x plus y equals b is tangent to the parabola, y equals a x squared, at x equals 5.
00:11
So let's just start off and say, well, y equals a x squared equals 5.
00:16
Let's find the equation of the tangent line.
00:18
And then let's make that equal to this and set some numbers equal to find a and b.
00:23
So i'm going to start off by saying, well, if x is 5, y, is going to be 25a.
00:30
Also, i can say y equals y not plus m times x minus x not.
00:37
That's the point slope form of the line.
00:38
We know x not and y not, that's 5 and 25a.
00:41
Well the m is going to be the slope that's going to be y prime, which is 2a x or 10a.
00:48
So y equals y not, that's going to be 25 a plus m which is 10 a times x minus x not, which is 5.
00:59
This point is going to be the equation of the tangent line.
01:04
So that's going to be 25a minus 50a...