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 wheels?

Answer 1

The answer is the attached figure

Explanation:

* Lets revise the equation of the circle

- The center-radius form of the circle equation is

(x – h)² + (y – k)2 = r², where the center is the point (h, k)

and the radius is r.

- This form of the equation is helpful, since you can easily find the

center and the radius.

* Now lets solve the problem

- The equation of the circle is (x + 2)² + (y - 0.5)² = 16

* Lets compare it with form above

∵ (x - h)² = (x + 2)²

∴ -h = 2 ⇒ × -1

∴ h = -2

∵ (y - k)² = (y - 0.5)²

∴ -k = -0.5 ⇒ × -1

∴ k = 0.5

∴ The center of the circle is (-2 , 0.5)

∵ r² = 16 ⇒ take √ for both sides

∴ r = √16 = 4

∴ The radius of the circle is 4 units

* Now lets look to the answer to find the circle whose center is

(-2 , 0.5) and radius 4 units

∴ The answer is the attached figure

* From the graph:

- The center of the circle is (-2 , 0.5)

- The horizontal diameter is between -6 and 2, then the length

of the diameter = 2 - -6 = 8

∵ The radius = 1/2 the diameter

∴ The raduis = 1/2 × 8 = 4 units