Transform the equation r−5⋅sin(θ) = 5⋅cos(θ) to an equation in x and y.

Question

A) x² + y² + 5y = 5x

B) x² + y² - 5y = 5x

C) x² + y² = 0

D) None of the above

Answer 1

r = 5 cos θ + 5 sin θ

r = 5 (x / r) + 5 (y / r)

r = (5x / r) + (5y / r)

r = (5x + 5y) / r

r² = 5x + 5y

x² + y² = 5x + 5y

Answer 2

Answer 3

r- 5sinx = 5cosx

r^2 = x^2 + y^2

x = rcosx

y = rsinx

r - 5y/r = 5x/r

r^2 - 5y = 5x

r^2 -5rsinx = 5rcosx

x^2 + y^2 -5y = 5x

B) is correct