Question

Determinar as coordenadas do centro e o raio das seguintes circunferˆencias:

a) (x + 2)² + (y − 3)² = 4

b) x² + (y + 7)² = 10

c) x² + y² − 6x + 4y − 12 = 0

c) 4x² + 4y² − 12x + 12y − 7 = 0

Answer 1

Resposta:

a) (x + 2)² + (y − 3)² = 4

C(-2,3) e r = 2

b) x² + (y + 7)² = 10

C(0, -7) e r = √10  

c) x² + y² − 6x + 4y − 12 = 0

x² - 6x + 9 - 9 + y² + 4y +  4 - 4 - 12 = 0

(x - 3)² + (y + 2)² = 25

C(3, -2) e r = 5

d) 4x² + 4y² − 12x + 12y − 7 = 0

x² - 3x + y² + 3y - 7/4

x² - 3x + (3/2)² - (9/4) + y² + 3y + (3/2)² - (9/4) - 7/4 = 0

(x - 3/2)² + (y + 3/2)² = 7/4 + 9/4 + 9/4

(x - 3/2)² + (y + 3/2)² = 25/4

C(3/2, -3/2) e r = 5/2