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The painted tiger moth is an insect lays bright blue eggs. Most of the time they lay their eggs in shrubs so their baby caterpillars can start to feed right away.
Moths lay eggs on ferns.
If they are oval shaped and in clusters they could be ladybug eggs, they are a darker yellow color.
giant water bugs
that would be termites
None do, what you heared or assumed is a myth.
An insect called Bed Bugs
Greenhouse Whiteflies are a pest that can occasionally be greenhouse pests. The greenhouse whirefly lays their eggs in a circular pattern.
CHICKEN
No, its an insect - it has 6 legs and lays eggs.
The Cicada
The female Lesser Water Bug fastens her eggs on the back of a male with glue. Other insects place eggs on plants or underneath the soil.