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

Answer:

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

Step-by-step 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:

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

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

$r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}$ --> $r=\sqrt{8+9sin^2(\theta)} +3sin(\theta)$