Help with Geometry (sphere) question

Question

Consider a sphere with the following equation:

$$(x - 9)^2 + (y + 5)^2 + (z - 2)^2 = 49$$

answer all the questions below

a. What is its center? b. What is its radius? c. True or false. (3, –3, 5) is on the sphere. yes I actually have never done a sphere problem and somehow my teacher expects me to turn it in tomorrow, that's why I need help, How can I get the center like do I input numbers in the variables.

Answer 1

Hint. Think about the distance formula in $\mathbb{R}^3$ (3 dimensional space). Then it should all become clear.

Answer 2

What is the difference between $y = x^2$ and $y = (x-1)^2$

Also, the graph of $y = x^2$ describes all the points $(x, y)$ such that $y = x^2$

These same principles can be applied to 3 dimension.

Answer 3

when you're given the equation of a sphere like $(x-a)^2 + (y-b)^2 + (z-c)^2 = R^2$ the center is $(a,b,c)$, the radius is $R$ and a point $(x_0,y_0,z_0)$ is on the sphere if and only if when you plug in the values you obtain a valid equality.