find an equation of the sphere with center (2,-6,4) and radius 5. Describe its intersection with each of the coordinates planes.

Question

find an equation of the sphere with center (2,-6,4) and radius 5.  Describe its intersection with each of the coordinates planes.

anonymous · Answer

so i know how to do the equation, but how do i do the intersection?

anonymous · Answer

$$(x-2)^2 + (y+6)^2 + (z-4)^2 = 25$$

hero · Answer

What course are you taking?

anonymous · Answer

calc 3

anonymous · Answer

the description of the intersection is an equation  of a circle i believe based on the example prior to this problem

amistre64 · Answer

|dw:1327252360580:dw|

amistre64 · Answer

you know the distance you are from the plane; you know the Radius of the sphere, so we can calculate the radius of the circle in the plane

amistre64 · Answer

the plane you pick is just dropping that variable from the picture to get your center in that plane:

(1,2,3) centers in no-x plane at (2,3)
                     the no-y plane at (1,3)
              and the no-z plane at (1,2)

amistre64 · Answer

the distance away from the plane is the one that you dropped :)

anonymous · Answer

okay so the xy plane would be (x-2)^2 + *y+6)^2 = 9

anonymous · Answer

The sphere does not intersect the y=0 coordinate plane.

anonymous · Answer

wait it would be = 16?

amistre64 · Answer

(2,-6,4) and radius 5

xy: no-z:  center at (2,-6)  with a distance of 4

radius in no-z = sqrt(5^2-4^2)

anonymous · Answer

ohhh okay okay

anonymous · Answer

wait still confused

anonymous · Answer

so what would be the equation for yz?

hero · Answer

How do I unsubscribe from this?

amistre64 · Answer

yz: no-x plane; centers on (y,z)  with a radius of:  sqrt(5^2 - x^2)

anonymous · Answer

so 25-4? root 21?

amistre64 · Answer

yep

amistre64 · Answer

and r^2 = 21 then in your equation of circle stuff

anonymous · Answer

but how would i do xz?

anonymous · Answer

r = root(25-36)

amistre64 · Answer

well, it centers in the no-y so (x,z);  its radius is then sqrt(5^2-y^2)

amistre64 · Answer

yep

anonymous · Answer

but its a negative number

amistre64 · Answer

it is isnt it :)  tell me; if your stretching to reach 5 and your 6 away, do you hit it?

anonymous · Answer

yeah bc r =6?

amistre64 · Answer

|dw:1327252967020:dw|

anonymous · Answer

oh so it never intersects?

amistre64 · Answer

its negative meaning there is no real radius in that plane so we aint even touching it

anonymous · Answer

so there wouldn't be an equation for xz

amistre64 · Answer

correct; the xz plane has no intersection with the sphere

anonymous · Answer

awesome! thank you so much!

amistre64 · Answer

yep