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

Question

asked Dec 13, 2023 210k views

2 Answers

Altso · Answer 1 · 2023-12-19T12:52:21+0000

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:

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

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

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

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

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

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

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