If the Netgear has "repeater mode" it's quite simple. And you don't have to have it "plugged in" to the cable co's "modem/wifi router". In fact plugging it in to a LAN port (via an Ethernet Cat5e or 6 cable) would just allow you to use the Netgear as a true AP (access point). This is actually the preferred method of extending your network, i.e., by using a separate wifi router as an AP. But if laying down Ethernet cabling over a long distance or between floors and multiple walls throughout your home isn't possible or practical, you can use some wifi routers as wireless repeaters.
This does NOT require you to plug anything into your cable co modem/wifi router. Instead, you set the operating mode (of your Netgear in this example) to run in "Repeater Mode" and then just pick which SSID of your cable co router/wifi you want the Netgear to connect to so that it will repeat that signal, give the Netgear your SSID's password, and it will connect and then repeat the channel, thus extending your wifi coverage to more remote locations in your home, providing for broader coverage.
You do need to be mindful to locate your repeater in a location where it will be getting a strong signal from your cable co modem/wifi router, because you will lose throughput by repeating the signal. A repeater roughly halves the connection rate and throughput, so that client devices connecting to the repeater will get about half the speed they would otherwise if they were connecting directly to the cable co wifi router (but again, this also will extend your range to areas where you presently have no coverage at all). Depending on the speed you are receiving from your ISP, using a repeater may or may not be a deal-breaker. If your initial speed from the ISP is already very low, it will be even lower for those devices connected to the "repeater/extender". But if you have good speeds from your ISP (e.g., I'd say above 100 Mbps, but certainly above 50 Mbps if you intend to do any media streaming), you may not notice much difference, if any. In terms of internal media streaming, it all depends what you're trying to achieve and your particular environmental variables, which are unknown and thus none of us can truly predict what sorts of performance you will get in the real world.
And while you didn't ask, in addition to a wired remote AP, or a wireless extender, you might also want to look at using either Powerline (which uses the wiring in your home instead of Ethernet cabling...this can be hit or miss depending on how your home is wired, and it will also add costs because you need two Powerline adapters, one near your current router and the other where you want to place your AP), or MOCA adapters (MOCA uses the same coaxial cables that you may already also be using for your cable television....again, this can be costly and is also tricky to set up for many people...it's never quite caught on, but if you know what you're doing, it can be a terrific way to extend your network and internet connectivity to other areas of your home.).