Question

Hat is the radius of a circle whose equation is x2 + y2 – 10x + 6y + 18 = 0?

Answer 1

x² + y² - 10x + 6y + 18 = 0
- 18 - 18
x² + y² - 10x + 6y = -18
x² - 10x + y² + 6y = -18
(x² - 10x + 25) + (y² + 6y + 9) = -18 + 25 + 9
(x² - 5x - 5x + 25) + (y² + 3y + 3y + 9) = 7 + 9
[x(x) - x(5) - 5(x) + 5(5)] + [y(y) + y(3) + 3(y) + 3(3)] = 16
[x(x - 5) - 5(x - 5)] + [y(y + 3) + 3(y + 3)] = 16
[(x - 5)(x - 5)] + [(y + 3)(y + 3)] = 16
(x - 5)² + (y + 3)² = 16

The radius of the equation is 4.

Answer 2

`x^2+y^2-\underbrace{10x}_(2x\cdot\fbox5)+\underbrace{6y}_(2y\cdot\fbox3)\boxed{+18}=0\\\\the\ radius:\\r^2=5^2+3^2-18\\\\r^2=25+9-18\\\\r^2=16\\\\r=√(16)\\\\\boxed{r=4}`