Question

Find the center and radius of the given circle and graph it

2a. x^2+(y+5)^2=4

2b. x^2-6x+y^2+14y+33=0

Answer 1

2a)

$$x ^ {2} + (y + 5) ^ {2} = 4$$

The center: $x = 0, y = -5$

The radius: $R = 2$

2b)

$$x ^ {2} - 6 x + y ^ {2} + 1 4 y + 3 3 = 0$$ $$x ^ {2} - 6 x + 9 - 9 + y ^ {2} + 1 4 y + 4 9 - 4 9 + 3 3 = 0$$ $$(x - 3) ^ {2} + (y + 7) ^ {2} = 2 5$$

The center: $x = 3, y = -7$

The radius: $R = 5$