If you want to use awk (I did):
awk 'BEGIN { FS = "\n"; RS = "^\n" } $0 ~ pattern { print $0 }' file
Maybe awk is overkill for this, and someone may want to verify that "^\n" will match a blank line. Notice also that this prints the entire "paragraph" but you can print selective lines by changing "print $0" to some other record number.
This avoids a useless use of cat, as well.