rewrite in polar form x^2+y^2-6y-8=0
r^2=6r+6sin theta +8
r^2=6rsin theta +8
r^2=6r+6cos theta +8
r^2=6r cos theta +8
To rewrite the equation \(x^2 + y^2 - 6y - 8 = 0\) in polar form, we can use the following equations:
\[x = r \cos \theta\]
\[y = r \sin \theta\]
Substituting these equations into the original equation, we have:
\[(r \cos \theta)^2 + (r \sin \theta)^2 - 6(r \sin \theta) - 8 = 0\]
\[r^2 \cos^2 \theta + r^2 \sin^2 \theta - 6r \sin \theta - 8 = 0\]
Since \(\cos^2 \theta + \sin^2 \theta = 1\), we can simplify the equation further:
\[r^2 - 6r \sin \theta - 8 = 0\]
Therefore, the polar form of the equation \(x^2 + y^2 - 6y - 8 = 0\) is \(r^2 - 6r \sin \theta - 8 = 0\).