Question

A manufacturer is designing a two-wheeled cart that can maneuver in tight spaces. On one test model, the wheel placement (center) and radius are modeled by the equation (x + 2)^2 + (y - 1)^2 = 16. Which graph shows the position and radius of the wheels? thank you :)

Answer 1

Given:

From the equation of a circle,

`(x-h)^2+(y-k)^2=r^2`

The following can be deduced when the two equations are compared.

`\begin{gathered} h=-2 \\ k=1 \\ r^2=16 \\ r=√(16) \\ r=4 \\ \\ Hence,\text{ the center of the circle is at }(h,k)=(-2,1) \\ The\text{ radius of the circle is }r=4 \end{gathered}`

Thus, the graph that has a radius of 4 and a center of (-2,1) is;

Therefore, the answer is ;