Find an equation of the conic in a rotated x'y'-system without an x'y' term. (Use xp for x' and yp for y'.)

Question

x² + 12xy − 8y² − 1 = 0

Answer 1

cot 2θ = (A - C) / B

Determine θ

Use the following conversions

x' = x cos θ + y sin θ

y' = -x sin θ + y cos θ