Mathematics, 22.09.2019 15:00 xemnas1994

Gfind an equation of the sphere with center (3, −10, 4) and radius 5. (x−3)2+(y+10)2+(z−4)2=25 use an equation to describe its intersection with each of the coordinate planes. (if the sphere does not intersect with the plane, enter dne.)

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Answer from: anthonybowie99

The Equation of the sphere with center (3, -10, 4) and radius 5 is correctly given as:

(x-3)^2+(y+10)^2+(z-4)^2=5^2

,

The x-y axis is the set of all points (ordered triples) of the form (x, y, 0), where x, y can be any point, but the z-coordinate is 0.

the intersection of the sphere and this plane is found by letting z=0:

$(x-3)^2+(y+10)^2+(z-4)^2=5^2\\\\(x-3)^2+(y+10)^2+(0-4)^2=5^2\\\\(x-3)^2+(y+10)^2+16=25\\\\(x-3)^2+(y+10)^2=9\\\\(x-3)^2+(y+10)^2=3^2$

the last equation is the standard equation of the circle with center (3, -10) and radius 3.

Indeed, we expect the intersection of a sphere with a plane to be a circle.

Similarly the y-z plane is represented by (0, y, z) and the x-z plane by (x, 0, z),

The intersection of the sphere with the plane y-z is:

$(0-3)^2+(y+10)^2+(z-4)^2=5^2\\\\(y+10)^2+(z-4)^2=25-9=16=4^2$

and the intersection of the sphere with the x-z plane is :

$(x-3)^2+(0+10)^2+(z-4)^2=5^2\\\\(x-3)^2+(z-4)^2=25-100\ \textless \ 0$

which makes no sense since the left hand side is positive (or at least 0).. This means that there is no intersection of the sphere with the x-z plane.

intersection with the x-y plane: (x-3)^2+(y+10)^2=3^2

intersection with the y-z plane: (y+10)^2+(z-4)^2=4^2

intersection with the x-y plane: none

Answer from: Quest

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

Answer from: Quest

Ithink if im not mistaking b is -3 but im not a 100% sude
Can someone and explain this problem to me? : d

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Gfind an equation of the sphere with center (3, −10, 4) and radius 5. (x−3)2+(y+10)2+(z−4)2=25 use a...

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