Asymptotes of a hyperbola

The  exercise appears under the Precalculus Math Mission. This exercise explores the hyperbola specifically concentrating on the equations of the asymptotes of a hyperbola.

Types of Problems
There is one type of problem in this exercise:


 * 1) Write the asymptotes of the hyperbola in point-slope form: This problem provides a hyperbola equation written in standard form. The student is expected to use this form to find the equation of the asymptotes and write those equations in the template provided.Aoah1.png

Strategies
Knowledge of powers of various numbers would be a great advantage on this problem, especially regarding speed badges.
 * 1) The line is expected in point-slope form, i.e., $$y-y_1=m(x-x_1)$$.
 * 2) The slope will be the square root of the number under y^2 divided by the square root of the number under x^2.
 * 3) The x entry will be the value seen in the equation, whereas the y entry will be the opposite of what is seen.

Real-life Applications

 * 1) Hyperbolas are conics and so they have many applications to optics and acoustics.
 * 2) Hyperbolic mirrors dissipate light.