Question

Exercises 2–4

2. Identify the center and radius for each of the following circles.
a. x^2−20x+y^2+6y=35
b. x^2−3x+y^2−5y=19/2

Answer 1

for a .center is -2,2 and the radius is 5

for b. center is -2,3 and the radius is 9

Explanation:

Answer 2

The answer to your question is below

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 =
`√(144) = 12`

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 =
`√(18)`