Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant? Describe process.

Question

psymon · Answer

I'm new to this stuff too, so someone will correct me if I'm wrong xD If it is in the first octant, then the maximum radius we can have without going outside of the 1st octant would be 4, since our y-coordinate is only 4 units away. So that being said, we just need to know that the equation for a sphere is
$$(x-x _{0})^{2}+(y-y _{0})^{2}+(z-z _{0})^{2}=r ^{2}$$
So just filling in the blanks, we could just plug in each coordinate into the appropriate part of the equation and also know that the radius of 4 squared will be 16. So this would then give us
$$(x-5)^{2}+(y-4)^{2}+(z-9)^{2} = 16$$

anonymous · Answer

r = 4, center at given point...

raffle_snaffle · Answer

how do you know the radius r=4?

psymon · Answer

Because the conditions say that it has to be in the first octant. Any radius greater than that will push the edges of the sphere into another octant.

raffle_snaffle · Answer

I am thinking right now.

anonymous · Answer

suppose r > 4, and x = z = 0

raffle_snaffle · Answer

The first octant?

psymon · Answer

Well, the question said contained in the first octant O.o

anonymous · Answer

3 dimensions... each has a + & - direction => 2^3 = 8 octants

anonymous · Answer

like 2d has 4 quadrants

psymon · Answer

|dw:1376178408346:dw|