Question

a manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, the wheel placement (center) and radius are modeled by the equation (x+2)^2+(y-0.5)^2=16. Which graph shows the position and radius of the wheel?

Answer 1

1) Equation given:

(x+2)²+( y-0.5)² = 16

2) Circumference equation

Remember that the equation of a circumference is:

(x - a)² + ( y - b)² = r²

Where a and b are the coordinates of the center (a,b) of the circle, and r is the radius.

That let's you infere from the given equation, (x+2)²+( y-0.5)² = 16, that the center is (-2, 0.5) and the radius is 4.


And with that you can do the graph: it is a circumference of radius 4 with center ( 2, - 0.5). You can see it in the figure attached.

Answer 2

The general equation of the circle is
(x - h)² + (y - k)² = r²
Where (h,k) represents the coordinates of the center of the circle
and r represents the radius of the circle.
Comparing the general equation with the given equation which is:
(x+2)²+(y-0.5)²=16
∴ h = -2 , k = 0.5 , r² = 16 ⇒⇒⇒ r = 4
the coordinates of the center of the circle = (h,k) = (-2,0.5)
the radius of the circle = r = 4

The graph which shows the position and radius of the wheel is attached.