1. How to identify and graph them.
Conic Sections
How to identify and graph them.

2. Identifying Conic Sections
A quadratic relationship is a relation specified by an equation or inequality of the form:
Ax2 +Bxy + Cy2 + Dx + Ey + F = 0
Where A, B, C, D, E, & F are constants.
The following information assumes that B=0. Therefore there is no xy-term.
To IDENTIFY what conic section you have:
Look at the coefficients of x2 and y2.

3. There are five types of conic sections you need to worry about.

4. Circles
The coefficients of x2 and y2 have the same sign and same value.
An example of a circle is x2 + y2 = 16.
In this example x2 and y2 have coefficients equal to positive 1.

5. Ellipses
The coefficients of x2 and y2 have the same sign but different values.
An example of an ellipses is
9x2 + 25y2 = 225
In this example the coefficient of x2 is positive 9. The coefficient of y2 is positive 25.

6. Hyperbolas
The coefficients of x2 and y2 have different signs and different values.
An example of a hyperbola is
16x2 - 9y2 = 144
In this example the coefficient of x2 is positive 16. The coefficient of y2 is negative 9.

7. Parabolas
Parabolas are “special” conic sections. There are two types parabolas that you will need to graph.

8. Y-Direction Parabolas
Y-Direction Parabolas open in the y-direction.
Y-Direction Parabolas are defined by the general formula
y = ax2 + bx + c
An example of a Y-Direction Parabola is:
y = 2x2+4x-3

9. X-Direction Parabolas
X-Direction Parabolas open in the x-direction.
X-Direction Parabolas are defined by the general formula
x = ay2 + by + c
An example of a X-Direction Parabola is:
x = 4y2+yx-2

10. That’s all folks!