Classifying Conic Sections Dr. Shildneck Fall, 2015

General Second Degree Equation The equation of any conic can be written in the form Which is called the general second-degree equation in x and y. The expression is called the discriminant of the equation and can be used to determine which type of conic the equation represents.

Classifying Conics If the graph of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 is a conic, then the type of conic can be determined as follows: Discriminant Type of Conic B2 – 4AC < 0, and A = C Circle B2 – 4AC < 0, and A ≠ C, (or if B ≠ 0) Ellipse B2 – 4AC = 0 Parabola B2 – 4AC > 0 Hyperbola If B = 0, each axis of the conic section is horizontal or vertical. If B ≠ 0, the axes of the conic are rotated (not horizontal/vertical). Thus, for “regular” conics, there is no xy-term in the equation.

Example 1: Classify and write in standard form.

Example 2: Classify and write in standard form.

Example 3: Classify and write in standard form.

Example 4: Classify and write in standard form.

ASSIGNMENT Alternate Text (from blog) Page 689 Exercises #49 – 58 ALL (Classify and Put each conic in standard form.)