3. For all $m, n$ satisfying $1 \leqslant n \leqslant m \leqslant 5$, the number of different hyperbolas represented by the polar equation $\rho=\frac{1}{1-C_{m}^{n} \cos \theta}$ is
A. 15
B. 10
C. 7
D. 6
The polar equation of a conic section is $\rho=\frac{e p}{1-e \cos \theta} \Rightarrow e=C_{m}^{n}>1$. Since $1 \leqslant n \leqslant m \leqslant 5 \Rightarrow C_{m}^{n}=2,3,4,6,5,10$ for a total of 6 values, so the answer is $D$.