\f\f\fGravity 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: orbit of less massive star center focal of mass point orbit of more massive star For the above system, we place the center of mass at the origin. The equations for the two stars' orbits are: 16x2 + 192x + 576 + 25y = 1600 16x2 - 96x + 144 + 25y = 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