Answer:
The answer to your question is below
Step-by-step explanation:
a) x² - 20x + y² + 6y = 35
Complete perfect squares
x² - 20x + y² + 6y = 35
x² - 20x + (10)² + y² + 6y + (3)² = 35 + (10)² + (3)²
Factor (x - 10)² + (y + 3)² = 35 + 100 + 9
Simplify (x - 10)² + (y + 3)² = 144
Center = (10, -3)
radius = [tex]\sqrt{144} = 12[/tex]
b) x² - 3x + y² - 5y = 19/2
Complete squares
x² - 3x + y² - 5y = 19/2
x² - 3x + (3/2)² + y² - 5y + (5/2)² = 19/2 + (3/2)² + (5/2)²
Factor (x -3/2)² + (y - 5/2)² = 19/2 + (3/2)² + (5/2)²
Simplify (x - 3/2)² + (y - 5/2)² = 19/2 + 9/4 + 25/4
(x - 3/2)² + (y - 5/2)² = 38/4 + 9/4 + 25/4
(x - 3/2)² + (y - 5/2)² = 72/4
(x - 3/2)² + ( y - 5/2)² = 18
Center = (3/2, 5/2)
radius = [tex]\sqrt{18}[/tex]
