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5. Convert the rectangular equation x² + y² - 6y = 0 into a polar equation.

A. r = 6 sin theta
B. r = 6 cos theta
C. r = √6 sin theta
D. r = √6 cos thea​

2 Answers

3 votes

Answernone

none

none

Explanation:

User Anil Kumar C
by
7.6k points
3 votes

Answer:

A. r = 6 sin theta

Explanation:

Given equation is:
x^2+y^2-6y=0....(1)

Using the formulae that link Cartesian to Polar coordinates.


x=r\cos\theta \: and \: y = r\sin\theta

Plugging the values of x and y in equation (1), we find:


(r\cos\theta)^2+(r\sin\theta)^2-6(r\sin\theta)=0


\implies r^2\cos^2\theta+r^2\sin^2\theta-6r\sin\theta=0


\implies r^2(\cos^2\theta+\sin^2\theta)=6r\sin\theta


\implies r^2(1)=6r\sin\theta


(\because \cos^2\theta+\sin^2\theta=1)


\implies( r^2)/(r)=6\sin\theta


\implies\huge{\purple{ {r}=6\sin\theta}}

User Altso
by
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