8-1

In section One chapter Eight, we learned how to find the angle of inclination.
For a line, m= tan alpha
If A doesn't equal C for a conic, use tan 2 alpha = B/A-C
If A does equal C for a conic, use alpha = pi/4
Ax^2 + By + Cy^2 + Dx + Ey + F = 0
alpha = angle of inclination
To the nearest degree, find the inclination of line
2x + 5y = 15
line = m = tan alpha
-2/5 = tan alpha
alpha = tan ^ -1 (2/5)
alpha = 21.801
Then one must take the alpha and move it to section II and IV
To go from I to II subtract 180
To go from I to IV and make negative then add 360
So in the end, the answer is
Alpha = 158.199 and 338.199
Find the direction of angle alpha,
X ^2 – 2xy + 3y^2 = 1
First find out if A = C
Since 1 does not 3 you must use the formula tan 2 alpha = B/A-C
So, tan 2 alpha = -2/1-3
Then, tan 2 alpha = 1
2 alpha = tan ^-1 (1)
2 alpha = 45, 225
So, alpha = 22.5 and 112.5