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:

`(\mleft(+8\mright)^2)/(36)-(\mleft(-2\mright)^2)/(49)=1`

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

`((y-d)^2)/(a^2)-((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=-(a)/(b)=-\frac{\sqrt[]{36}}{\sqrt[]{49}}=-(6)/(7) \\ m_2=(a)/(b)=(6)/(7) \end{gathered}`

We can graph them as:

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