Gravity holds objects in space together. It makes the moon orbit our planet, and it makes the planets in our solar syste

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Gravity holds objects in space together. It makes the moon orbit
our planet, and it makes the planets in our solar system orbit the
sun. In some parts of space, gravity can make two stars appear to
orbit each other, and when this happens, we call the pair “binary
stars.” In reality, both stars orbit a center of mass outside of
their individual masses, as shown below:



For the above system, we place the center of mass at the origin.
The equations for the two stars’ orbits are:

16x2+192x+576+25y2=1600
16x2−96x+144+25y2=400

a) Determine whether the equations represent parabolas, hyperbolas,
or ellipses.
b) Write both equations in standard form, and show how you arrived
at your answers. Which equation matches with each orbit? How do you
know?
c) Although these two stars are unlikely to crash, at how many
points on their orbits would such an event be possible? Explain how
you would find those points.
orbit of less massive star center of mass focal point orbit of more massive star