Question

Convert the equation from Rectangular to Polar form: y2 = 9x.

Answer 1

Answer:

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$r = 9 \cotθ \cscθ$

ѕtєp вч ѕtєp єхplαnαtíσn...

The conversion from rectangular to polar,

$x = r \cosθ \\ y = r \sinθ \\ \\ substitute \: for \: x \: and \: y, \\ \\ \\ ({r \sinθ})^{2} = 9(r \cosθ) \\ r {}^{2} \sin {}^{2} θ = 9r \cosθ \\ r {}^{2} \sin {}^{2}θ - 9r \cosθ = 0 \\ r(r \sin {}^{2} θ - 9 \cosθ )= 0$

at this point...

either r = 0

or

r sin²θ - 9 cos θ = 0

lєt'ѕ ѕσlvє thє ѕєcσnd σnє tσ gєt α mєαníngful αnѕwєr~

$r \sin {}^{2} θ = 9 \cosθ \\ r = \frac{9 \cos θ}{ \sin {}^{2} θ } \\ r = \frac{9 \cosθ }{ \sinθ } \times \frac{1}{ \sinθ } \\ \\ remember..... \\ \frac{cosθ}{sinθ}=cotθ \: \: and \: \:\frac{1}{ \sinθ } = \cscθ \\ \\ r = 9 \cotθ \cscθ$

hope helpful~

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