J pole with feedline impedance other than 50 ohms

[wa2ise]

Oh, there's tons of instructions on how to make a J pole antenna fed by 50 ohm coax. But there's absolutely nothing I can find if you want to use feedline of some other impedance, say 75 ohm coax, 300 ohm twinlead, 450 ohm ladderline, or even a twisted pair in ethernet cat 5 cable (100 ohms balanced, I ran some to extend a POTS phone line, and had a leftover twisted pair, and hey, Cat 5 runs in the VHF spectrum anyway, but not on this cat 5 cable or else the FM radio would suffer too much leakage). This must be classified or something...

As a scientific wild @$$ guess (SWAG) it looks like you can locate the feedpoints for these other feedline impedances by taking the square root of the ratio of (desired impedance/50 ohm), and taking that resulting number and multiply it by the length from the bottom (shorted end of the J pole) the instructions tell you to place the 50 ohm coax connections. It seems to work on a J pole I made for my FM broadcast receiver, though I realize there's a ton of variables, like receiver mismatches, stray conductors near the antenna and so on.

Yes, I know that all ham rigs are 50 ohm, and thus why noone ever says anything about any other impedance location. But if I wanted to make a J pole to receive say an FM broadcast station at 101.1 MHz and couple it to the 75 or 300 ohm FM tuner input, I'd want to know where these impedances exist on a J pole antenna.