Question

What are the slopes of the asymptotes for the hyperbola(+8)^2/36−(−2)^2/49=1

Answer 1

We have a rational expression:

$\frac{\mleft(+8\mright)^2}{36}-\frac{\mleft(-2\mright)^2}{49}=1$

This is the equation of an hyperbola with a horizontal axis of symmetry:

$\frac{(y-d)^2}{a^2}-\frac{(x-e)^2}{b^2}=1$

There are two asymptotes and we have to find the slopes of them.

Using the generic equation of the hyperbola, we can express the slopes of the asymptotes as:

$\begin{gathered} m_1=-\frac{a}{b}=-\frac{\sqrt[]{36}}{\sqrt[]{49}}=-\frac{6}{7} \\ m_2=\frac{a}{b}=\frac{6}{7} \end{gathered}$

We can graph them as:

Answer: the slopes are m1=-6/7 and m2=6/7.