### Instruction: The hyperbola given by the equation \[\frac{x^2}{100} - \frac{y^2}{64} = 1\]has asymptotes $y = \pm mx,$ where $m$ is positive. Find $m.$.### Response: I recall that the standard form of a hyperbola centered at the origin with horizontal transverse axis is \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1,\]where $a$ and $b$ are the semi-major and semi-minor axes, respectively.
The asymptotes of such a hyperbola are the lines $y = \pm \frac{b}{a} x.$
Comparing the given equation with the standard form, I see that $a^2 = 100$ and $b^2 = 64.$
Therefore, $a = 10$ and $b = 8.$
Substituting these values into the formula for the asymptotes, I get $y = \pm \frac{8}{10} x.$