Q: Help with Geometry (sphere) 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.

A: 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.

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

A: 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.
