Powered Miata Antenna Q's

I just received this antenna for my birthday:

http://ecommerce.mossmotors.com/p/miata-mx-5/miata-exterior/antennas/raked-shorty-antenna/906-185-MIA-1

Now my question: It has a plug for 12 VDC. Should I connect it to the aftermarket CD player's powered antenna lead? I thought that was for powered antennas that go up and down on their own, not an antenna that needs power???...

So far it works slightly better than the broken off stubby rubber one that I removed to install this one.

Does anyone have this antenna?

If I do have to run power to it, should I run it all the way back to the head unit's powered antenna lead or right to the battery that is 6" away?

http://easycalculation.com/physics/electromagnetism/antenna-wavelength.php

By playing around a bit with that & a calculator, it looks like a 7 inch mast antenna is tuned to about 87MHz if you're looking at a 1/20th wavelength. But then again the actual antenna element is probably not the full length of the external mast, so maybe it's closer to 90MHz. This is still below the FM band on most radios. Curious who did the engineering on this.

Or maybe there's something that I'm missing, and there's some RF smarty guy on here that can inform me of where I've messed up, but from what I'm seeing this isn't a very good car antenna. It is also odd that the product page doesn't give power requirement information or anything to really tell you what's going on. If I were to make a guess, there's a small RF amplifier in the thing, otherwise I'm not sure what power would be used for at an antenna like that.

Edit: p.s. I would not constantly power this device, you don't want an antenna amplifier pulling constant load on a battery, and if you do give this thing power I would put a fuse or circuit breaker inline with the thing very near the power source (either the head unit or some kind of switched setup from the battery).

http://en.wikipedia.org/wiki/Whip_antenna#Electrically_short_whips

Or I'm forgetting the bit I know about antennas. There an RF engineer in the house?

Chances are that the antenna might have a built-in amp, hence the need for power.

I'd hook it up to the antenna power connection at the radio, you don't want the antenna to be "live" all the time, especially if you don't DD the car.

Does the antenna coaxial cable run down the center console from the trunk to the dash?

Yeah, the power antenna lead should have enough amperage available for a small amp if it is normally used for powering an antenna mast motor.