Question

Write down an (in)equality which describes the solid ball of radius 2 centered at (-2, 5, 2). It should have a form like ????2 ????2 (????−2)2−4>

Answer 1

$\text{We know that the euation of the sphere with radius r and centered at (h,k,l)}\\ \text{is given by:}\\ \\ (x-h)^2+(y-k)^2+(z-l)^2=r^2\\ \\ \text{here we have given a solid ball of radius 2 centered at }(-2, 5,2), \text{ so the }\\ \text{region of the ball will be all the area within the ball.}\\ \text{Hence the inequality that will describe the ball is give given by}$

$(x-(-2))^2+(y-5)^2+(z-2)^2\leq 2^2\\ \\ \Rightarrow (x+2)^2+(y-5)^2+(z-2)^2\leq 4\\ \\ \text{hence the required inequality that describes the ball is:}\\ \\ (x+2)^2+(y-5)^2+(z-2)^2-4\leq 0$