Question

Eliminate 0 from the following: 

x = 4cos θ – 5sin θ, y = 4sin θ + 5cos θ

Answer 1

x = 4cos θ – 5 sin θ … (i) 

y = 4sin θ + 5cos θ .. .(ii) 

Squaring (i) and (ii) and adding, we get 

x² + y² = (4cos θ – 5sin θ)² + (4sin θ + 5cos θ)² 

= 16cos² θ – 40 sinθ cosθ + 25 sin² θ + 16 sin² θ + 40sin θ cos θ + 25 cos² θ 

= 16(sin² θ + cos² θ) + 25(sin² θ + cos² θ) 

= 16(1) + 25(1) 

= 41