Determine the center and radius of the following circle equation: x2 + y2 + 18x – 18y + 113 = 0
2 answers:
Answer:
centre = (- 9, 9 ), radius = 7
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 18x - 18y + 113 = 0
Collect the x and y terms together and subtract 113 from both sides
x² + 18x + y² - 18y = - 113
To obtain standard form use the method of completing the square.
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(9)x + 81 + y² + 2(- 9)y + 81 = - 113 + 81 + 81
(x + 9)² + (y - 9)² = 49 ← in standard form
with centre = (- 9, 9 ) and r = = 7
You might be interested in