Question

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​

Answer 1

Answernone

none

none

Explanation:

Answer 2

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}}`