Question

Determine o centro C e a medida R do raio das circunferências a seguir a) x² - 6x + y² - 8y = 144 b) x² + y² - 6x – 2y = 0

Answer 1

a)x2−6x+y2−8y−144=0

(1)⋅x2+(−6)⋅x+(y2−8y−144)=0

x=−(−6)±(−6)2−4⋅(y2−8y−144)−−−−−−−−−−−−−−−−−−−−−−√2

x=6±36−(4y2−32y−576)−−−−−−−−−−−−−−−−−−√2

x=6±−4y2+32y+612−−−−−−−−−−−−−−−√2

x=6±(2)⋅−y2+8y+153−−−−−−−−−−−−−√2

x=(2)⋅[(3)±−y2+8y+153−−−−−−−−−−−−−√](2)

x1=3+−y2+8y+153−−−−−−−−−−−−−√

x2=3−−y2+8y+153−−−−−−−−−−−−−√

b)2−6x+y2−2y=0  

(1)⋅x2+(−6)⋅x+(y2−2y)=0

x=−(−6)±(−6)2−4⋅(y2−2y)−−−−−−−−−−−−−−−−−√2

x=6±36−(4y2−8y)−−−−−−−−−−−−−√2

x=6±−4y2+8y+36−−−−−−−−−−−−−√2

x=6±(2)⋅−y2+2y+9−−−−−−−−−−−√2

x=(2)⋅[(3)±−y2+2y+9−−−−−−−−−−−√](2)

x1=3+−y2+2y+9−−−−−−−−−−−√

x2=3−−y2+2y+9−−−−−−−−−−−√