10 kHz bandwidth at 10 MHz is very tight for a R-L-C filter. Even if you could put a high enough order filter together, it would be useless due to part tolerance errors.
The only passive way to do this that has any chance of working is to use a 10 MHz crystal. You should still preceed it with a L-C filter to eliminate frequencies that can make the crystal resonate at overtones (harmonics). The L-C pre-filter will also help reduce the power of the signals the crystal has to get rid of.
There is another way, but it is definitely active and more complex, and uses the technique of hetrodyning. The basic concept is to shift the original frequency to a lower value where the desired bandwidth is a much larger fraction of the frequency, then shift the result back. The relatively wider bandwidth at the lower frequency makes a filter more tractable. Old AM radios used this technique, but didn't bother shifting back since they only wanted the amplitude and could get that from the shifted frequency.
450 kHz was a common IF (intermediated frequency) for AM radios intended to receive the commercial AM band from about 550 kHz to 1.7 MHz. The tuning knob would adjust the local oscillator, which needed to be 450 kHz less than the reception frequency. The result would go thru a 450 kHz narrow band filter and amplifier. This needed about 20 kHz bandwidth, which is 4.4% of 450 kHz. That was doable with a few carefully factory-tuned parts. In "super hetrodyne" radios, the tuning knob also adjusted a L-C filter to roughly select the RF frequency of interest. Note that due to how product modulation works (which is how the local oscillator was "mixed" with the filtered RF), there are actually two RF frequencies that result in the 450 kHz IF. These are the local oscillator plus 450 kHz (the desired RF frequency), and the local oscillator minus 450 kHz, called the "image" frequency. The original L-C filter on the RF needed to be tight enough to eliminate the image frequency before the hetrodyning.
You should also consider what you want to do with the final narrow band signal. If you just want to AM detect it, for example, then there may be other ways than starting with a very narrow band filter. It's not worth going into this without more information about what exactly you are trying to do, where this 10 MHz signal is coming from, what kind of modulation you want to detect, how much out of band noise the input signal contains, etc.
Since this is not an answer, it should be a comment. But, this "comment" is too long and detailed for a comment.
(1) The equations for the filter in the 3rd image do not include the effect of load resistor in the 1st image schematic.
(2) This is not so much a bandpass filter but, rather, the sum of a 2nd order low-pass and a 1st order bandpass (as can be seen by writing the transfer function as two separate fractions).
(3) I'm not sure what "corner frequency" is in this context. For a high-pass or low-pass filter, the context is clear. For this, I'm not so sure.
Have you left out some details of the problem?
(Also, did you put all this off to nearly the last minute?)
Best Answer
Neither options seem very reasonable in 2019.
You'd want to do your localization in digital anyway, so do the filtering in digital, too.
You don't need very much bandwidth by modern standards. In fact, this would be pretty trivial to build with but a cheap soundcard (e.g. the one integrated in your PC/Laptop/shmartphone) with few external components.
You'd want to use your sound card to sample the hydrophones. Now, sadly, soundcards are meant for humanly audible sound, so you can't use them to pick up 37.5 kHz (or even higher) directly.
What's easily possible, however, is frequency-mixing your 37.5 kHz and 45 kHz down to lower frequencies that you can, in fact, easily pick up with a sound card. Then, in software, throw some bandpass filters at the problem – software bandpass filters can be arbitrarily steep (given that audio sampling rate signal processing doesn't pose a serious load for any modern smart phone or PC).
So, what you'd want to do is
Tadah, you've just built a superheterodyne receiver for hydrophones, with IF filtering implemented in software, where filters are free and trivial to construct precisely, and for location purposes very importantly, with linear phase and thus defined group delay. That's not even possible with RC/LC/RLC, mathematically!
A down-mixer is just any nonlinear device (e.g. a diode) that you feed with the sum of the LO and the high-frequency signal. Then, the result is low-pass filtered (single-stage RC filter), to eradicate all the harmonics you don't want.
If you're able to do a bit of digital design yourself: get a microcontroller with as many ADC channels as you need. You can do bandpass subsampling to directly mix down the signals with (multiples of) the sampling frequency. That would still require you to do a very rough analog bandpass filter, but definitely minimize the complexity of your design.