Conic Sections How to identify and graph them

Conic Sections How to identify and graph them.

Identifying Conic Sections © A quadratic relationship is a relation specified by an equation or inequality of the form: Ax 2 +Bxy + Cy 2 + 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 x 2 and y 2.

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

Circles © The coefficients of x 2 and y 2 have the same sign and same value. © An example of a circle is x 2 + y 2 = 16. © In this example x 2 and y 2 have coefficients equal to positive 1.

Ellipses © The coefficients of x 2 and y 2 have the same sign but different values. © An example of an ellipses is 9 x 2 + 25 y 2 = 225 © In this example the coefficient of x 2 is positive 9. The coefficient of y 2 is positive 25.

Hyperbolas © The coefficients of x 2 and y 2 have different signs and different values. © An example of a hyperbola is 16 x 2 - 9 y 2 = 144 © In this example the coefficient of x 2 is positive 16. The coefficient of y 2 is negative 9.

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

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

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

That’s all folks!