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Ahat [919]
4 years ago
14

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

Mathematics
2 answers:
fredd [130]4 years ago
6 0

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

Arisa [49]4 years ago
3 0

<u>Answer:</u>

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

<u>Step-by-step explanation:</u>

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)

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