What is the diameter for this given equation? (x^2+24) + (y^2+4y)=85

The answer to your question is  2√233  ≈ 30.5

Step-by-step explanation:

Data

                  (x² + 24x    )  + (y² + 4y    ) = 85

Process

1.- Complete the perfect square trinomials

                 (x² + 24x +  (12)²) + (y² + 4y + (2)²) = 85 + 12² + 2²

2.- Simplify

                 (x² + 24x + 144) + (y² + 4y + 4) = 85 + 144 + 4

                 (x + 12)² + (y + 2)² = 233

3.- Calculate the radius

                 radius² = 233

                  radius = √233

                 diameter = 2radius

                 diameter = 2√233  ≈ 30.5