we gonna find GOLDFISH!

• -m=tan α where m is the slope of a line and α (alpha or goldfish if you prefer)is the angle of inclination




• tan 2α = (B)/(A-C) finds the angle of inclination for a conic. Ax^2 + Bxy + Cy^2 + .. =


• A short cut that they don't want you to know for a conic if A = C then α = pi/4 , 5pi/4

Ex1. To the nearest degree find the angle of inclination for -2x + 4y = 8.
First you have to solve for y. so you get y = (1/2)x + 2
Now you use the formula for a line. m =tan α
1/2 = tan α
arctan(1/2) = α
26.565 degrees and 206.565 degrees
So goldfish equals 26 degrees 33 minutes 54 seconds and 206 degrees 33 minutes 54 seconds

Ex2. Identify the graph of the equation and find the angle of inclination for x^2 + 2y^2 - 3x + y = 11

B^2 -4AC

0 -4(1)(2)

-8

Ellipse

tan 2α = (B)/(A - C)

tan 2α = (0)/(1-2)
tan 2α = 0
arctan(o) = 2α

o = α

Ex 3. Find the angle of inclination. 3x^2 + 5xy + 3y^2 - 5x + y = 4

From the shortcut we know that when A = C the angle of inclination is pi/4 , 5pi/4 so the answer is

α = pi/4 , 5pi/4

AND THAT'S HOW YOU FIND GOLDFISH!

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