Use following substitutions:
r cosθ = x
r sinθ = u
r² = x² + y²
r = 8 cosθ + 4 sinθ
Multiply both sides by r
r² = 8 r cosθ + 4 r sinθ
x² + y² = 8x + 4y
This is equation of circle. We can put in standard form:
x² − 8x + y² − 4y = 0
x² − 8x + 16 + y² − 4y + 4 = 16 + 4
(x − 4)² + (y − 2)² = 20
Circle centered at point (4, 2) with radius = √20
