Circles

1. $\rhd$ Pythagorean Theorem and Radii of Circles (5:52)Finds missing segments of triangles within a circle using the Pythagorean Theorem.
2. $\rhd$ Standard Equation of a Circle (6:18)Equation for the points $(x,y)$ on a circle with radius $r$ and center $(h,k)$.
3. $\rhd$ Features of a circle from its equation in standard form (3:50)
Finding the center and radius of a circle from the equation in standard form.  Given $(x+3)^2 + (y-4)^2 = 49$, find the center and radius. Solution: center is $(-3,4)$ and radius is $7$.
4. $\star$ Features of a circle from its equation in standard form.
Find the center and radius of $x^2 + (y-2.25)^2 = \frac{169}{196}$.
5. $\rhd$ Features of a circle from its expanded equation (4:20)Graph the circle $x^2 + y^2 + 4x - 4y - 17 = 0$ (Puts the equation into standard form by completing the square.)
6. $\star$ Features of a circle from its expanded equation.Find the center and radius of the circle $x^2 + y^2 - 6x - 6y +2 = 0$

PatrickJMT:

1. $\rhd$ Finding the Center-Radius Form of a Circle by Completing the Square – Example 1
2. $\rhd$ Finding the Center-Radius Form of a Circle by Completing the Square – Example 2
3. $\rhd$ Finding the Center-Radius Form of a Circle by Completing the Square – Example 3