Key Concepts:
- Standard Form – The equation of a circle is ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) is the center and (r) is the radius.
- Completing the Square is used to rewrite a general equation in standard form to find the center and radius of a circle.
- Transformations of Circles – A circle is shifted up/down/left/right when the center coordinates in its equation is modified.
Skills Covered:
- Identifying center and radius from an equation.
- Rewriting equation of a circle in standard form using completing the square.
- Modifying a circle's equation for translations.
Example Problem:
- Find the equation of a circle centered at ((-3, 2)) that passes through ((1, 2)).
- The equation of a circle is (x^2 - 2x + y^2 + 6y = 26). Find the radius of the circle.