What is the radius for this given equation? (x^2+10x) + (y^2-8y) = 59

The answer to your question is r = 10

Step-by-step explanation:

Data

(x² + 10x) + (y² - 8y) = 59

Process

1. - Complete the perfect square trinomials

(x² + 10x + (5) ²) + (y² - 8y + (4) ²) = 59 + (5) ² + (4) ²

2. - Simplify

(x² + 10x + 25) + (y² - 8y + 16) = 59 + 25 + 16

3. - Factor

(x + 5) ² + (y - 4) ² = 100

or (x + 5) ² + (y - 4) ² = 10²

4. - Compare the result with the standard form

(x - h) ² + (y - k) ² = r²

then r² = 10²

and r = 10