Write the polar equation r = -16 sin θ in rectangular form

Question

It's r = -16 sin theta in rectangular form 

Answer 1

Use the formulas:  x = rcosθ, y = rsinθ, x² +y² = r^2.

 

Since r = -16sinθ, we have r² = -16rsinθ

 

So, x² + y² = -16y

 

x² + y² + 16y = 0

 

x² + (y² + 16y + 64) = 64

 

(x-0)² + (y+8)² = 8²

 

This is the circle with center (0,-8) and radius 8.  

 

Answer 2

Hi TJ,

 

Coordinate conversion equations are 

y = rsin(theta), r = sqrt(x^2 + y^2), and  r^2 = x^2 + y^2

r = -16sin(theta) 

r^2 = -16rsin(theta)

x^2 + y^2 = -16y

x^2 + y^2 + 16y = 0 (complete the square for y^2 + 16y by adding (16/2)^2 to both sides)

x^2 + y^2 + 16y + 64 = 0 + 64

x^2 + (y+8)^2 = 64

This represents a circle with center at x=0 and y=-8 with a radius of 8 units.