Unit 5
Circle relationships and the wider family of curves that come from slicing a cone. Completing the square is the recurring technique.
Lesson 5.1
An inscribed angle is half the measure of its intercepted arc. A central angle equals its intercepted arc measure. A radius perpendicular to a chord bisects it; tangent segments from a common exterior point have equal lengths.
Lesson 5.2
A circle is the set of points a fixed distance from a center. Read the center after writing the equation in squared form. Complete the square in both variables to convert an expanded equation.
Lesson 5.3
Standard forms distinguish circles, ellipses, parabolas, and hyperbolas. For an ellipse, the larger denominator gives the major axis. For a hyperbola, the positive squared term gives the transverse-axis direction.
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