Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}

You are given the equation 36 = 9x² + 4y². You are asked to find the slopes of the asymptotes of the hyperbola. A hyperbola has the following general equation x²/a² + y²/b² = 1. the goal here is to find the slopes of the hyperbolic equation. So divide both sides by 36

36 = 9x² + 4y²
(1/36)[36 = 9x² + 4y²]
1 = x²/4 + y²/9
a² = 4
a = 2
and
b² = 9
b = 3

To find the slope, divide a/b and you will get 2/3.

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°