Question

Write the equation of the circle with the given center and radius.

Answer 1

Step-by-step explanation:

The standard equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$

Center = (h, k)

#1

Center = (0,2)

h = 0

k = 2

r = 5

$(x - h)^2 + (y - k)^2 = r^2$

$(x - 0)^2 + (y - 2)^2 = 5^2$

#2

Center = (-4,-5)

h = -4

k = -5

r = $\sqrt{2}$

$(x - h)^2 + (y - k)^2 = r^2$

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

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

#3

Center =(-1,3)

h = -1

k = 3

r = 8

$(x - h)^2 + (y - k)^2 = r^2$

$(x - (-1))^2 + (y - 3)^2 = 8^2$

$(x + 1)^2 + (y - 3)^2 = 8^2$

#4

Center: (9,0)

h = 9

k = 0

r = $\sqrt{3}$

$(x - h)^2 + (y - k)^2 = r^2$

$(x - 9)^2 + (y - 0)^2 = \sqrt{3}^2$