Question

Help please!

A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, the wheel placement (center) and radius is modeled by the equation (x + 1.5)^2 + (y + 1)^2 = 9. What is the graph that shows the position and radius of the wheels?

Answer 1

Equation of a circle is given by (x - a)^2 + (y - b)^2 = r^2; where (a, b) is the centre and r is the radius.
(x + 1.5)^2 + (y + 1)^2 = 9
(x - (-1.5))^2 + (y - (-1))^2 = 3^2
Center = (-1.5, -1) and radius is 3.

Answer 2

we know that

The equation of the circle is of the form

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

where

`(h,k)` is the center

`r` is the radius

in this problem

we have

`(x+1.5)^(2) +(y+1)^(2) =9`

`(x+1.5)^(2) +(y+1)^(2)=3^(2)`

So

the center is the point
`(-1.5,-1)`

the radius is
`3` units

using a graph tool

see the attached figure