45. The Cartesian equation for the polar curve \( r = \sin \theta \) is






Answer is: option2

\( x^2 + y^2 = y \)

Solution:

If \( r = \sin \theta \), we multiply both sides by \( r \) to obtain \( r^2 = r \sin \theta \).

To convert to Cartesian coordinates, we replace \( r^2 \) with \( x^2 + y^2 \) and \( r \sin \theta \) with \( y \).

This gives \( x^2 + y^2 = y \).

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