Question

Use the information provided to write the equation of each circle. *photo attached

Answer 1

Answer:

( x + 13 )^2 +  ( y + 6 )^2 = 1; Option A

Step-by-step explanation:

~ The question we have at hand is: x^2 + y^2 + 26x + 12y + 204 = 0 ~

Let us apply the circle equation ( x - a )^2 + ( y - b )^2 = r^2 ⇒ provided r is the radius, centered at point ( a, b )

1. First rewrite x^2 + y^2 + 26x + 12y + 204 = 0 in the standard form of circle equation: x^2 + y^2 + 26x + 12y + 204 = 0

2. Now move the loose number to the right side: x^2 + 26x + y^2 + 12y = -204

3. Let us now group variables: ( x^2 + 26x ) +  ( y^2 + 12y ) = -204

4. Convert x to square form: ( x^2 + 26x + 169 ) +  ( y^2 + 12y ) = -204 + 169

5. Convert to square form: ( x + 13 )^2 +  ( y^2 + 12y ) = -204 + 169

6. Convert y to square form: ( x + 13 )^2 +  ( y^2 + 12y + 36 ) = -204 + 169 + 36

7. Convert to square form, and simplify: ( x + 13 )^2 +  ( y + 6 )^2 = 1

Answer: ( x + 13 )^2 +  ( y + 6 )^2 = 1