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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.

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1  
What are your thoughts on the problem? Is this your first encounter with the equation of a sphere? Telling us what you have tried will helps us determine how we can best help you. –  AWertheim Aug 8 '13 at 1:35
    
You don't need to know about spheres to know that in order to find out whether the point $(3,-3,5)$ is on the graph of an equation, you plug in $3$ in place of $x$, $-3$ in place of $y$, and $5$ in place of $z$, and then see whether the equality that you get is true or not. –  Michael Hardy Aug 8 '13 at 2:03

3 Answers 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.

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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.

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

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Do you really think the OP is going to know what $\mathbb{R}^3$ means? –  Ron Gordon Aug 8 '13 at 1:44

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