Answer:
-X² + Y² = 2√2 Y
Explanation:
xy = x + y
When rotated to a XY coordinate system:
x = X cos θ + Y sin θ
y = -X sin θ + Y cos θ
Given θ = π/4:
x = X (√2/2) + Y (√2/2)
y = -X (√2/2) + Y (√2/2)
x = (√2/2) (X + Y)
y = (√2/2) (-X + Y)
Substitute:
xy = x + y
(√2/2) (X + Y) (√2/2) (-X + Y) = (√2/2) (X + Y) + (√2/2) (-X + Y)
(1/2) (X + Y) (-X + Y) = (√2/2) (X + Y − X + Y)
(1/2) (-X² + Y²) = √2 Y
-X² + Y² = 2√2 Y
