Algebra 2 conic sections

Question

1.A rabbit will move no more than 10 miles away from its hole. At that time, you are taking a walk about 6 miles west and 7 miles south of the rabbit hole. Is there any possibility of you meeting the rabbit? Show all work.

2.what is the center of the ellipse 4y^2 +16x = -x^2? Write your answer in simplified, rationalized form. Show all work.

Answer 1

Part 1) When you are in the position described you are sqrt(85) miles from the hole.

Part 2 Complete the square on x to get the center as (-8,0).