Family Overview

In Plain Language

Topic 4.6 represents conic sections analytically with horizontal or vertical symmetry.

• Parabola: vertex (h, k); opens up/down as y - k = a(x - h)^2 or left/right as x - h = a(y - k)^2 (4.6.A.1).
• Ellipse: center (h, k) with (x - h)^2/a^2 + (y - k)^2/b^2 = 1; a circle has a = b (4.6.A.2).
• Hyperbola: center (h, k); opens left/right or up/down in standard form; has asymptotes (4.6.A.3).

Course scope only (Unit 4 additional topic; not on the AP Exam).

Why It Matters

Conic equations connect implicit graphs (4.5) to parametrization (4.7) and modeling contexts.

How Families Can Help

• Name the conic type first: parabola, ellipse, or hyperbola.
• Read (h, k) as center or vertex from standard form.
• Sketch key points before full technology graph.

What Not to Do

• Do not swap plus/minus signs between ellipse and hyperbola forms.
• Do not treat a circle as unrelated to the ellipse family.
• Do not ignore which variable is squared first for opening direction.