Math Geek :
it's not the active adapter that's the issue. that is only for the newest gen cards that have removed the analog signal completely like the nvidia 1000 and amd 4/500 series.
i'm gonna guess the problem i 2 fold, one you're trying to output a resolution the ps4 is not able to. it is designed for tv's so likely only supports tv type resolutions such as 720p or 1080p.
second is that this is a sony product and they make no apologies for making EVERYTHING proprietary. i'd look and see if they sell a ps4 branded hdmi to vga adapter. if they do, this tells you they likely added a chip to the output to ensure you could not use off the shelf stuff with the ps4.
all the ps's have been like this and the ps4 is nothing new for this
He needs an active adapter, that is the problem. It needs to be a powered active adapter to convert the signal due to the cards removing analog signals.
I have used and verified the following product to do exactly what you request.
Again the reason why it also most likely would not display is due to low powered HDMI ports, typically from a card.
https://www.amazon.com/Cable-Matters-HDMI-Adapter-Black/dp/B00879DM56
This does what you need and has a micro USB power in the back which is optional and typically only used for conversions to and from analog signals. Like exactly what you are attempting to do.