Question

What is the diameter of the circle ?

2x^2+2y^2-20x-20y-22=0
Write your answer in simplified, rationalized form.

Answer 1

The answer to your question is diameter =
`2√(61)`

Explanation:

2x² + 2y² - 20x - 20y - 22 = 0

Solution

2x² - 20x + 2y² - 20y = 22

2(x² - 10x ) + 2(y² - 10y ) = 22

Complete perfect square trinomials

2(x² - 10x + 5²) + 2(y² - 10y + 5²) = 22 + 50 + 50

Factorize

2(x - 5)² + 2(y - 5)² = 122

(x - 5)² + (y - 5)² = 61

radius =
`√(61)`

diameter = 2r

diameter = 2
`√(61)`