1. Classifying Conic Sections
Fall, 2017

2. 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.

3. Classifying Conics
If the graph of Ax2 + Bxy + Cy2 + Dx + Ey + F = 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.

4. Example 1: Classify and write in standard form.

5. Example 2: Classify and write in standard form.

6. Example 3: Classify and write in standard form.

7. Example 4: Classify and write in standard form.

8. ASSIGNMENT
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Exercises #44 – 53 ALL