At present, the polar coordinate problems in the college entrance examination are all directly processed.

The polar coordinates of the problem N are (a*Pi/2, Pi/2), and the polar coordinates of M are (a* 13Pi/6, 13Pi/6). Note that m is the second intersection of the ray OM and the spiral, so the angle is 9Pi/4.

In rectangular coordinates, x=r*cos angle, y=r*sin angle.

Then, n is (0, a*Pi/2) and m is (a* 13Pi radical number 3/ 12, a * 13pi/ 12).

But if the topic goes through polar coordinates (2,2Pi), then 2=a*2Pi, that is, Pi*a= 1.

Then, n is (0, 1/2) and m is (13 radical 3/ 12, 13/ 12).

Calculate the result with the two-point distance formula (root number 139)/6.