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transform the following polar equation into an equation in rectangular coordinates r=-4...
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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.
Posted by sciencesolve on November 21, 2012 at 6:34 AM (Answer #1)
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