Weekly Math Problem #80

Equation of a Circle. We're definitely keeping our algebra skills sharp with this week's problem. 🧠 As the saying goes, "Repetition is the mother of all learning". So, you will definitely see skills being repeated in the problems as well the combination of them to solve the problems. The equation of a circle is part of a larger topic called conic sections. Let's  go!  🏃🏿‍♀️

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

       ✔️     Substitution
       ✔️     Completing the square technique
       ✔️     How to solve a quadratic equation

            

WMP #80 wants us to...

Happy solving!

Check back on Saturday, April 9th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Part a.

To determine the center and radius of the circle, the completing the square technique needs to be used on the given equation. To start that process, the constant needs to be isolated. Once the equation is in standard form, then the center and radius can be identified.

The center of the circle is (1, -1) and its radius is 1 unit. This was figured out without graphing it. We'll view the graph later in this post.

Part b.

To show that the point (1, -2) is a point of intersection for circle C and the given line, the substitution method was used. The equation of the line was substituted for y in the equation of the circle. The equation of the circle was then simplified into a factorable quadratic equation. This allows for values of x to be solved for...one of which is the x-value in the given point. It is then shown that the corresponding y-value is indeed the y-value in the given point.

Now that we've completed both parts of the problem, let's view the graph:

**This plot was created using Geogebra's Graphing Calculator. Click image to enlarge.

 

▪️ Did you use the same methods above to solve the problem? If so, please share.

▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. ✏️
Let's move on to WMP! #81. 💪🏿

Cheers!

The Younge Lady