More hyperbola and ellipse

Today in class we discussed more facets of ellipses and hyperboles. In other words, we learned how to write equations and draw both kinds of figures when given only a certain amount of starting information (ex. verticies and foci, center and foci, asymptotes, etc.).

-Also, we learned that "a" and "b" simply represent distances from the center of the figure.

-Where the asymptotes intersect on a hyperbola is the center of the hyperbola.

This is mostly useful information for our quiz on Thursday, Feburary 12th.

Conic Sections: Hyperbolas

In class today, we reviewed out second conic section: hyperbolas.

Hyperbolas act like the opposite of ellipses. Rather than adding the x and y terms in the standard form of the equation, we subtract them. Rather than subtracting a^2 and b^2 to find the foci, we add them.


We reviewed the "box" method of graphing in which we can draw a rectangle centered at (h,k) with length 2b and width 2a. This can be used to draw the desired asymptotes/vertices in the graph.

Pay close attention to the point-slope method to find the asymptotes and the way we decide what direction a hyperbola goes.


Finally, we reviewed how to change a messed-up equation in the form:

Ax^2+Bx+Cy^2+Dy+E=0

into standard form at the end of class(where A or C are negative).





Whenever you want to graph a hyperbola: label vertices, foci, asymptotes(show box work)