Answer:
(x + 5)² + (y + 2)² = 120
Explanation:
You need two pieces of information to write the equation of a circle, the center and the radius. This was given in the question so you can just use the following fill-in-the-blank formula to write the equation.
If the center is (h, k) and the radius is r, fill them in here:
(x - h)² + (y - k)² = r²
For your question the center is (-5, -2) and r is√120.
You do need to already know that "minus-a-negative" IS the same as "plus-a-positive" (that's why the final answer has + inside the parentheses) ALSO, you need to know that square and squareroot un-do each other. So if you square sqrt120, you just get "plain" 120. That is, (sqrt120)² is 120.
Fill in the center and radius:
(x - h)² + (y - k)² = r²
(x - -5)² + (y - -2)² = (√120)²
Simplify.
(x + 5)² + (y + 2)² = 120
Taaa-daaa! that's it! Don't you think more people would hate formulas less if they were sold as "fill-in-the-blank" and "shortcuts" !?! I think so!