Question

Cartesian expression to polar equation.
Correct?

Answer 1

Polar curve, given:
\(\Large r=8\sin\theta\)

I multiply times r on both sides,
\(\Large r^2=8r\sin\theta\)

we know that in general
\(\Large r^2=y^2+x^2\) and \(\Large y=r\sin\theta\)

So, in this case we have:
\(\Large r^2=8r\sin\theta~~~~\Longrightarrow~~~~\Large y^2+x^2=8y\)

Answer 2

\[r = 8 \sin \theta\]\[r^2 = 8 r \sin \theta\]\[x^2 + y^2 = 8y\]\[x^2 + y^2 - 8y = 0\]\[x^2 + (y - 4)^2 - 16 = 0\]\[x^2 + (y - 4)^2 = 4^2\]