26.16 The curve determined by the polar equation $\rho=\frac{1}{1-\cos \theta+\sin \theta}$ is
(A) a circle.
(B) an ellipse.
(C) a hyperbola.
(D) a parabola.
(Chinese High School Mathematics League, 1982)
［Solution］The original equation simplifies to
$$
\rho=\frac{1}{1-\sqrt{2} \cos \left(\theta+\frac{\pi}{4}\right)} .
$$

Given the eccentricity $e=\sqrt{2}>1$, we know it is a hyperbola. Therefore, the answer is $(C)$.