Convert r=5/3sinθ−cosθ to rectangular form

Question

how would i go about doing this? in general i know what to do but not with fractions!

Answer 1

Multiplying by r we get r² = 5/3rsinθ - rcosθ; or x² + y² = 5/3y - x; after completing squares we get:

(x + 1/2)² + (y - 5/6)² = 1/4 + 25/36; (x + 1/2)² + (y - 5/6)² = 34/36

If condition is r = 5/(3sinθ - cosθ) then multiplaying by denominator we get: 3rsinθ - rcosθ = 5 and we get

3y - x = 5