Question

Find the center, radius, and intercepts of the circle given below and then sketch the graph of the circle.

x²+(y-1)^2=1

Answer 1

Center (0, 1)

Radius 1

x-intercept (0, 0)

y-intercept (0, 0), (0, 2)

Explanation:

(1) A circle that has center (a, b) and radius r can have the equation as below:

(x - a)^2 + (y - b)^2 = r^2

Re-write the original equation: x^2 + (y - 1)^2 = 1, we have:

(x - 0)^2 + (y - 1)^2 = 1^2

=> The center of this circle: (a, b) = (0, 1) and the radius r = 1

(2) To find out the x-intercept, we substitute y = 0 into original equation.

=> x^2 + (0 - 1)^2 = 1

=> x^2 + 1 = 1

=> x^2 = 0

=> x = 0

=> x-intercept (0, 0)

(3) To find out the y-intercept, we substitute x = 0 into original equation.

=> 0^2 + (y - 1)^2 = 1

=> (y - 1)^2 = 1

=> y - 1 = -1 or y - 1 = 1

=> y = 0 or y = 2

=> y-intercept (0, 0) and (0, 2)

Hope this helps!