How to find capture area of an engine inlet?
It is not so hard, actually.
You need to know the speeds ahead and inside the intake. You can deduce their ratio from the pressure recovery factor, and normally the Mach number inside the intake is between 0.4 and 0.5, so this, combined with your design flight speed, is a good starting point.
In supersonic flow the air is rammed into the intake face, producing a shock. This will be a straight shock in case of a pitot intake or an oblique shock in case of an intake ramp. Use the appropriate shock tables to find the corresponding speed and density ratios.
For subsonic flow you can use a Gedankenexperiment: Your intake is flying through a densely packed array of stream tubes. Some of them will end up inside the intake, others will be pushed aside as they come close to the intake lip and will flow around it. The speeds in those tubes varies between flight speed well ahead of the intake and your eventual intake speed inside the intake. In between, things change continuously in subsonic flow or via shocks in supersonic flow. Now assume that all the air which passes through the intake will have to pass through their corresponding stream tubes, both ahead and inside the intake. No air is allowed to cross between tubes. If the air inside the intake flows faster than flight speed, the flow in the tubes will be accelerated as they approach the engine face, so the intake has to ingest a lot of tubes to keep mass flow the same. Conversely, if flight speed is higher than intake speed, some of the tubes will be pushed aside to get a match between the mass flows ahead and inside the intake. Don't forget to adjust stream tube area for density changes: The change in stream tube cross section has to be inversely proportional to the change in air density as the air inside the steam tube changes speed, like this:
$$\frac{\delta\rho}{\rho}=-Ma^2\cdot\frac{\delta v}{v}$$