Circles

Khan Academy:

  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