FINAL GEOMETRY QUESTION!! PLEASE HELP

Step-by-step explanation:

The error was in Step 2.  The student attempted to "complete the square" by adding 4 to x^2 + 4x and then subtracting 4 from the other side of the equation.  

The work, if done correctly, would look like this:

x^2 + 4x + 4 - 4 = -y^2 + 20.

This condenses to:

(x + 2)^2 - 4 + y^2 = 20

(x + 2)^2 + y^2 = 24

This circle has its center at (-2, 0) and its radius is √24 = √4√6, or 2√6

You'll find it easier to understand if you illustrate the problem as what is shown in the attached picture. From the illustration and the problem description, two equations can be formulated:

HJ = 2JK
HJ + JK = HK

2JK + JK = 78
3JK = 78
JK = 78/3
JK = 26