Question

When converting the polar equation r = 4sin(®) to Cartesian coordinates, which of the following represents the geometric meaning of the resulting equation?
* 1 point
A circle with center at (2, 0) and radius 2, derived from the identity r2 = x2 + y? and
r• cos(0) = x
• A line passing through the origin with slope 4
• A parabola opening upward with vertex at the origin
A circle with center at (0, 2) and radius 2, derived from the identity r = x? + y? and
r•sin(0) = y

Answer 1

r = 4 sin θ

Multiply by r: r^2 = 4r sin θ. Using r^2 = x^2 + y^2 and r sin θ = y gives
x^2 + y^2 = 4y ⇒ x^2 + (y − 2)^2 = 4.

So the curve is a circle with center (0, 2) and radius 2 (the last option).