Question

transform the following polar equation into an equation in rectangular coordinates r=-4 sin theta.A. x=-4y
B. x+y= -4
C. y= -4
D. x^2+(y+2)^2=4

Accepted Answer

You should remeber that you may convert the polar coordinates into rectangular coordinates using the following formulas such that:
sin theta = y/r => y = r sin theta
cos theta = x/r => x = r cos theta
x^2 + y^2 = r^2
The problem provides the information that r = - 4 sin theta , hence, multiplying by r both sides yields:
r^2 = -4r sin theta => r^2 = -4y
Substituting x^2 + y^2  for r^2  yields:
x^2 + y^2 = -4y
You should move -4y  to the left side such that:
x^2 + y^2 + 4y = 0
You need to complete the square y^2 + 4y  adding 4 both sides such that:
x^2 + y^2 + 4y + 4 = 4
You need to convert the expansion y^2 + 4y + 4  into t he square of binomial such that:
x^2 + (y+2)^2 = 4
Hence, converting the polar form of equation into the rectangular form yields x^2 + (y+2)^2 = 4,  thus you need to select the answer D.

Math

transform the following polar equation into an equation in rectangular coordinates r=-4 sin theta. A. x=-4y B. x+y= -4 C. y= -4 D. x^2+(y+2)^2=4

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