Question

Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ

options include:

x^2+y^2 = 4y

x^2+y^2 = -4

x^2+y^2 = 4

x^2+y^2 = -4y

Answer 1

x^2 +y^2 = 4y

Explanation:

Using the usual translation relations, we have ...

r^2 = x^2+y^2

x = r·cos(θ)

y = r·sin(θ)

Substituting for sin(θ) the equation becomes ...

r = 4sin(θ)

r = 4(y/r)

r^2 = 4y

Then, substituting for r^2 we get ...

x^2 +y^2 = 4y . . . . . matches the first choice