Question

Rewrite in polar form x^2 + y^2 - 6y - 8 = 0

Answer 1

the correct answer is B. r^2=6r sin 0+8

Answer 2

The correct answer option is
`r^2-6rsin(\theta)=8`.

Explanation:

We are given the following equation and we are to rewrite it in polar form:

`x^2 + y^2 - 6y - 8 = 0`

`\left \{ {{x^2+y^2=r^2} \atop {y=rsin \theta}} \right.`

Here, we need to make a perfect square trinomial:

`[r^2-6rsin(\theta)+` ___
`^2]=8`

`6rsin(\theta)` --->
`2 .r.3.sin \theta`

Completing the square to get:

`r^2-6rsin(\theta)+[3sin(\theta)]^2-[3sin(\theta)]^2=8`

`[r-3sin(\theta)]^2=8+[3sin(\theta)]^2` -->
`[r-3sin(\theta)]^2=8+9sin^2(\theta)`

`r-3sin(\theta)=√(8+9sin^2(\theta))` -->
`r=√(8+9sin^2(\theta)) +3sin(\theta)`