Answer
Centre (0, 1); radius = 1
x-intercept = 0; y-intercepts = y=2, y=0
Work Step by Step
Let us write the equation of the circle in standard form (x - 0)² + (y - 1)² = (1)².
Compare this equation with the equation (x - h)² + (y - k)² = r² .
The comparison yields the information about the circle. We see that h = 0, k = 1 and r = 1.
The circle has center (0, 1) and a radius if 1 unit. To graph the circle first plot the center (0, 1). Since the radius is 1 unit, locate four points on the circle by plotting 1 unit to the left, to the right, up and down from the center. These four points can be used to sketch the graph.
To find the x-intercepts, if any, let y = 0 and solve for x.
x² + (0 - 1)² = 1.
x² + 1 = 1
x² + 1- 1 = 1 - 1 Subtract 1 from both sides
x² = 0
x = 0
The x-intercept is 0.
To find y-intercepts, if any, let x = 0 and solve for y.
(0)² + (y - 1)² = 1
y - 1 = ±1
If y - = 1
y - 1 + 1 = 1 + 1
y = 2
If y - 1 = -1
y - 1 + 1 = -1 + 1
y = 0
The y-intercepts are 2 and 0.
