Question

Which is the parametric form of the polar equation r=-3theta

A.x=3thats cos theta

Y=3theta sin theta

B.x=-3theta cos theta

Y=-3theta sin theta

C.x=-3cos theta

Y=-3 sin theta

D.x=-theta cos theta

Y=-theta sin theta

Answer 1

Answer:B

Explanation:

Given

`r=-3\theta`

so
`x=-3\theta \cos \theta \quad \ldots(i)`

and

`y=-3\theta \sin \theta \quad \ldots(ii)`

squaring and adding
`(i)` and
`(ii)` we get

`x^2+y^2=(-3\theta \cos \theta)^2+(-3\theta \sin \theta)^2`

`x^2+y^2=r^2=9\theta ^2\cos ^2 \theta +9\theta ^2\sin ^2 \theta`

`r^2=9\theta ^2`

`r=-3\theta`

for
`r` to be negative both
`x` and
`y` must be negative