Transform the following polar equation into an equation in rectangular coordinates:

r=-4sin(theta)

Question

Transform the following polar equation into an equation in rectangular coordinates: 

r=-4sin(theta)

kj4uts · Answer

attachment

kj4uts · Answer

Don't you use this equation y = r*sin(theta) or is how it is already set up?

kj4uts · Answer

Would the answer be C. x^2+(y+2)^2=4

anonymous · Answer

Answer would be C, yes, you are 100% correct :)

jdoe0001 · Answer

hmmm how did you get $\bf x^2+(y+2)^2=4$  anyway?

kj4uts · Answer

= 4sinθ 

Multiply both sides by r. 

 r² = 4rsinθ 

x² + y² = 4y 
 x² + y² - 4y = 0 
 x² + (y² - 4y + 4) = 0 + 4 

 x² + (y + 2)² = 4

kj4uts · Answer

@jdoe0001

jdoe0001 · Answer

yeap... that's exactly correct :)

jdoe0001 · Answer

so is a circle with a radius of 2, centered at (0 , -2)

kj4uts · Answer

@jdoe0001 now if the 4 was positive r=4sin(theta) would the answer be x² + (y - 2)² = 4 the difference being (y-2) instead of (y+2)?

anonymous · Answer

Again correct mister :)
You rock !

jdoe0001 · Answer

yeap

jdoe0001 · Answer

if the 4 were positive
that means as you move it over the left side, it'd turn into a -4y
so the middle term of the trinomial is negative, yielding then (y-2)

anonymous · Answer

yep. at that time the r=+4sin(theta)