DWG NO. 08 — Unit 8 of 10
4 online lessons · 1 in-person Review & Practice Day
Unit 2 graphed y = ax² + bx + c and called it a parabola without asking why that particular shape shows up. It turns out the parabola has cousins — the circle, the ellipse, and the hyperbola — and all four come from the same geometric source: slicing a cone with a plane at different angles. This unit gives each one a proper definition in terms of distance (from a center, or from one or two fixed points called foci), and shows how to read that definition straight off a standard-form equation.
The back half steps back and asks a more practical question: handed a general second-degree equation with no picture attached, how do you know which conic it is before you've done any algebra? Lesson 8.4 answers that by reading the coefficients alone, then finishes the job of converting to standard form by completing the square — a skill you've already used for circles, now applied across the whole family.
Circles and Ellipses
Standard-form equations for circles and ellipses, and reading center, radii, vertices, and foci from them.
→Parabolas
Defining a parabola by its focus and directrix, and writing its standard (vertex) form equation.
→Hyperbolas
Standard-form equations for hyperbolas, and finding vertices, foci, and asymptotes.
→Identifying and Classifying Conics from General Form
Reading a general-form equation's coefficients to classify its conic, then converting to standard form.
→Review & Practice Day 8 — bring your questions from lessons 8.1–8.4. You'll work practice problems, get feedback, and take the Unit 8 test.