Question

Find the cartesian equation of r = 8 sin thet + 8 cos theta

Answer 1

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