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Solve the given problems involving tangent and normal lines.On a particular drawing, a pulley wheel can be described by the equation $x^{2}+y^{2}=100$ (units in $\mathrm{cm}$ ). The pulley belt is directed along the lines $y=-10$ and $4 y-3 x-50=0$ when first and last making contact with the wheel. What are the first and last points on the wheel where the belt makes contact?

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 1

Tangents and Normal

Derivatives

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:40

Find equations of the tang…

00:58

Find equations for the lin…

09:36

Finding Equations of Tange…

07:53

01:30

01:01

04:54

Find equations of (a) the …

04:06

Find the lines that are ta…

02:58

Tangent Lines and Normal L…

05:08

Hi, this is Claire. So a section 3.3, number 36 of stories for a calculus book. So here we have our function. Why is equal to X squared minus Mexico, for we are given the courtroom at 10 and were asked to find the tension and normal line equation. So here is the attention and normal line. It's a linear function of both. So we're gonna find the derivative when, um Xs equal to one. So this is if we get the derby tive of X square minus X to the fourth, we will get the slope. So that's gonna be minus or X cubed. Ms. We're gonna find this one Xs equal to one in this equals negative too. And that is equal to our slope, which is represented by hey. And so if we plug it into this equation, we get why is equal to negative two acts plus B and using the coordinates 10 we get B as equal 222 and our attention equation is going to be cool to why go to negative to X plus two. Then we're gonna box are and sir, And if we're gonna find the normal line equation. We know that it's going to be the soap is going to be perpendicular. So the slope has to be just huh? That's gonna be our A And then our we're gonna plug it into our equation more equals X plus be. And then this is, um, our equation for the normal line. And since it passes the 0.10 we're gonna plug that in and we got B is equal to negative one house. Our equation for a normal line is why is equal to half of bets minus huh?

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