A manufacturer is designing a two wheeled card that can maneuver in tight spaces. On one test model, the wheel placement (center) and radius are modeled by the equation (x - 1)^2 + (y + 2)^2 = 4, Which graph shows the position and radius of the wheels?
As an AI language model, I cannot provide a graph here. However, I can explain how to interpret the equation (x - 1)^2 + (y + 2)^2 = 4 to determine the position and radius of the wheels.
The equation is in the standard form of the equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.
Comparing the given equation to the standard form, we can see that the center of the circle is (1, -2), and the radius is 2. This means that the wheels are positioned at a distance of 2 units from the center point (1, -2), and the wheels are tangent to the circle at the points where they touch the ground.
To visualize the position and radius of the wheels, you can plot the center point (1, -2) on a coordinate plane, and draw a circle with a radius of 2 units around that center point. The points where this circle intersects with the x-axis represent the positions where the wheels touch the ground.
The given equation, (x - 1)^2 + (y + 2)^2 = 4, represents a circle with center (1, -2) and a radius of 2 units. To graph this equation, we can plot the center point and then draw the circle with the given radius.
Here is the step-by-step procedure for graphing the equation:
Step 1: Plot the center point.
The center of the circle is at (1, -2). Mark this point on the coordinate plane.
Step 2: Determine the radius.
The radius of the circle is given as 2 units.
Step 3: Draw the circle.
Using the center point and the radius, draw a circle with a radius of 2 units around the center point.
The graph that shows the position and radius of the wheels should be a circle with center (1, -2) and a radius of 2 units.