Weekly Math Problem! #33

Equation of a Tangent Line. And I'm back with the first WMP! of 2021. New year, same goal--to solve various types of math problems regularly so that the ol' noggin 🧠 stays sharp! 💪🏿 Do you have any math goals for 2021? Drop them below ⬇️.

Since calculus is a fave, I thought I'd start this year with a calculus problem. (It'll help me with momentum). I don't recall if I have mentioned this before but, my first experience with calculus was in high school--12th grade. I was preparing for the AP exam so, we were provided with materials to aid us with preparation. Here is a picture of one of the books I used in high school and where this week's problem is coming from:

I was enough of a nerd 🤓 then hold on to the book for almost 20 years 👵🏿. 

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to find a derivative
        ✔️     How to find the equation of a line using given information

WMP! #33 wants us to...

Happy solving!

Check back on Friday, January 15th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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Just in case you're not familiar with type of equation we've been given in the problem, it is the equation of a circle, centered at the origin, with a radius of 13 units. We will use the method of implicit differentiation to find the derivative:

Now that we have a point and a slope, we can proceed to finding the equation of the tangent line: 

You can stop at this point, but let's take a few extra steps to write the equation in a "nicer" form:

We're done. Now, if you remember anything about from last year, you will recall that l like images. So, I would be remiss if I didn't add to this blog post an image of the circle and it tangent line at the point (5, -12):

**This plot was created using Geogebra's Graphing Gaclulator.

...And that's a wrap! The first WMP! of 2021 is complete. I am excited to keep going this year and see what what other types problems we can solve.

▪️ What kind of problems would you like to see this year??

▪️ Comment below with your responses and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Can you see it? WMP! #34 is next.

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Cheers!

The Younge Lady