A tuned Yagi can be used as the feed for a parabolic dish, including at 1420 MHz, but it is usually not the best choice.
The important point is that the Yagi is not being used in its normal role as a high-gain antenna. You would point its main beam toward the dish, with the Yagi positioned around the dish’s focal point:
incoming 1420 MHz
------------------------>
\ /
\ /
\ /
\ /
V
PARABOLIC DISH
/ \
/ \
/ \
/ \
^
|
focus
[ YAGI ]
<=========
|
|
coax
|
LNA
The difficulty is illumination. A conventional long Yagi has a fairly narrow forward beam. A dish feed normally needs a much broader radiation pattern so that it illuminates most of the reflector:
GOOD DISH FEED
\ | /
\ | /
\ | /
\ | /
\|/
FEED
_____|_____
/ \
/ DISH \
/_________________\
LONG YAGI
||
\||/
\/
narrow
beam
_____|_____
/ \
/ DISH \
/_________________\
Much of dish may be under-illuminated
So a short Yagi — perhaps 2 or 3 elements — can potentially make quite a reasonable experimental feed. A 13- or 17-element hydrogen-line Yagi, like the sort you’ve been using as a stand-alone 1420-MHz antenna, would generally have far too narrow a beam to illuminate a typical prime-focus dish efficiently.
There’s another complication: the Yagi’s phase centre needs to be positioned appropriately at the focus, and the metallic boom/elements and feedline can increase blockage and alter the pattern.
For your 1420-MHz dishes, I’d generally rank the approaches approximately:
1420 MHz PRIME-FOCUS DISH FEEDS
Suitability
Cantenna/
waveguide EXCELLENT +++++
Choke-ring
cantenna EXCELLENT +++++
Dipole +
reflector GOOD ++++
2-element
Yagi POSSIBLE +++
3-element
Yagi POSSIBLE +++
Long Yagi
(13-17 el.) POOR +
The dish’s f/D ratio is crucial, because it determines the beamwidth you want from the feed.