5. [5 points each] A planet orbits a star on the elliptical path 2 2 X 262 242 Meanwhile, an asteroid follows . {20017, 1441?) I I I (24, 12mm) the hyperbolic path 2 2 8 6 The star of this solar system is at the focus, (10,0). Here coordinates are measured in millions of meters. At a certain time, the planet is at the position (my) :(24, 120/13) and has an x coordinate decreasing at the rate of 4 million meters per day. At the same time, the asteroid is at the position (um) :(200/7, 144/7) and has a vcoordinate decreasing at the rate of 6 million meters per day. How fast is the distance between them changing at that time? d a) First, use the given information and the path of the planet to find _y. Round your answer to dt one decimal place. d b) Next, use the given information and the path of the asteroid to find u. Round your answer to dt one decimal place. 5. (Continued) c) Now let D be the distance between the points (x,y) and (um). Give the formula for .D2 and use it to find the distance between the planet and asteroid at the given time. Round your answer to one decimal place. of!) d) Now find , the rate of change of the distance between the planet and asteroid at the given dt time. Round your answer to one decimal place