Find the centre and radius or each of the following circles.
(i) x² + y² - 2x + 4y - 4 = 0
(ii) x² + y² - 6x - 8y - 24 = 0
(iii) 2x² + 2y² + 3x + 4y + 9/8 = 0
(iv) 4x² + 4y² - 24x - 8y - 24 = 0
Answers
Answer:
Step-by-step explanation:
Find the centre and radius or each of the following circles.
(i) x² + y² - 2x + 4y - 4 = 0
(ii) x² + y² - 6x - 8y - 24 = 0
(iii) 2x² + 2y² + 3x + 4y + 9/8 = 0
(iv) 4x² + 4y² - 24x - 8y - 24 = 0
Equation of circle
(x-a)² + (y-b)² = r²
a , b center
r = radius
(i) x² + y² - 2x + 4y - 4 = 0
x² + y² - 2x + 4y = 4
x² - 2x + 1 + y² + 4y + 4 = 4 + 1 + 4
(x-1)² + (y+2)² = 9
(x-1)² + (y+2)² = 3²
Center = (1 , -2) Radius = 3
(ii) x² + y² - 6x - 8y - 24 = 0
=> x² + y² - 6x - 8y = 24
=> x² -6x + 9 + y² - 8y + 16 = 24 + 9 + 16
=> (x-3)³ + (y-4)² = 7²
Center = (3 , 4) Radius = 7
(iii) 2x² + 2y² + 3x + 4y + 9/8 = 0
x² + y² + 3x/2 + 2y + 9/16 = 0
x² + y² + 3x/2 + 2y =- 9/16
x² + 3x/2 + 9/16 + y² + 2y + 1 = -9/16 + 9/16 + 1
=> (x - 3/4)² + (y + 1)² = 1²
Center = (3/4 , -1) Radius = 1
(iv) 4x² + 4y² - 24x - 8y - 24 = 0
x² + y² - 6x - 2y - 6 = 0
x² + y² - 6x - 2y = 6
x² - 6x + 9 + y²- 2y + 1= 6 + 9 + 1
(x -3)² + (y -1)² = 4²
Center = (3 ,1) Radius = 2