There are actually several different images of constellations that appears in Contact at various different times. The most prominent are he constellation Lyra which contains the star Vega from which the alien signal emanates, the constellation of the Plough and the constellation of Corona Boreallis.

Taken together they appear to be a metaphor for Ellis's search for meaning and contact throughout her life.

The flashback scene during which a young Ellie and her father are watching the Persied Meteor shower which is associated with the plough (Big Dipper) is one of the most significant. When Ellie's father collapses the plough can be scene in spilled popcorn on the floor. In the DVD comentary track Jodie Foster makes a passing reference to it but I no longer have that disc so cannot add more detail.

The computer screens in the VLA controlled room for obvious reasons show many images of Lyra which contains Vega.

[![screen shot of Lyra on the VLA computer screens][1]][1]

It has often been said that the constellation Corona Borealis was Carl Sagans favourite constellation because of its apparent resemblance to the shape of a radio telescope. I cannot find a direct quote but this is repeated in many different places on the web. It certainly is the constellation that appears in sand in Ellie's fathers hand.

It's likely significance is that it acts as a metaphor for Ellie's search for meaning and contact in her life, even as an invitation to keep exploring, as in "take my hand I will help you on your way" which is what the aliens are trying to do. That said exactly how you interpret that metaphor will always be a little bit dependant on the viewer.

You can see a star map showing both Lyra and Corona Borealis here...

https://www.skyatnightmagazine.com/advice/hercules-constellation/


  [1]: https://i.sstatic.net/vSL9a.jpg