Conic Sections Problem solving

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

These are beginnings. You should show some work

Perimeter of rabbit are:

x² + y² = 25

Equation of your path

y = -7x/6 - 7

Determine the common solution and answer

x² + 16x + 16 + 4y² = -16

Now factor to determine center.