I don't believe Julian.

I don't believe you. It's clearly not orange. However, since your team won at the movie game, I'll let it slide. α maybe. :P OFF TOPIC. YAAAAY.

Anyway, angles of inclination.
For lines, you will use the formula m = tan(α), where m is the slope of the line.
For conics, you will use tan 2α = (B)/(A-C) where Ax^2+Bxy+Cy^2+...

Your angle of inclination will be α.

For those who forget or never knew, a slope of a line in the form of ax+by = c, is (-a/b). You could also solve the equation for y.
The slope of a line in the form of y = mx+b, is m.

You can use a handy dandy trick that works where A=C for conics. The angle of inclination will be π/4, and 5π/4.

Ex.1

Find the inclination of the line 3x+5y = 8.

• It's a line, so you'll be using the formula m = tanα.
• m=slope, and slope = -a/b, so m = -3/5.
• Plugging in, -3/5 = tanα.
• To solve, you have to take the inverse of both sides.
  tan^-1(-3/5) = α
• tan^-1(3/5) = 30.964, tan is negative in quadrants II and IV.
  
• tan^-1(-3/5) = 149.036 and 329.036
  
• α = 149°2'9'' and 329°2'9''

Ex.2
Identify the graph of x^2-xy+2y^2=2 and find the angle of inclination.

• A = 1, B = -1, C = 2
• B^2-4(A)(C) = -7
• It's negative and A does not equal C, so it's an ellipse.
• You will use tan2α = (B)/(A-C)
• tan2α = -1/-1 = 1
  
• Ignore the 2 in front of α for now and take the inverse.
• tan^-1(1) = 45°
• tan is positive in quadrants I and III.
• tan^-1(1) = 45° and 225°
• NOW you divide by 2.
  
• α = 45/2° and 225/2°

The game.

GG guys.