anonymous
  • anonymous
find an equation of the sphere with center (2,-6,4) and radius 5. Describe its intersection with each of the coordinates planes.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
so i know how to do the equation, but how do i do the intersection?
anonymous
  • anonymous
\[(x-2)^2 + (y+6)^2 + (z-4)^2 = 25\]
Hero
  • Hero
What course are you taking?

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anonymous
  • anonymous
calc 3
anonymous
  • anonymous
the description of the intersection is an equation of a circle i believe based on the example prior to this problem
amistre64
  • amistre64
|dw:1327252360580:dw|
amistre64
  • amistre64
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
  • amistre64
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
  • amistre64
the distance away from the plane is the one that you dropped :)
anonymous
  • anonymous
okay so the xy plane would be (x-2)^2 + *y+6)^2 = 9
anonymous
  • anonymous
The sphere does not intersect the y=0 coordinate plane.
anonymous
  • anonymous
wait it would be = 16?
amistre64
  • amistre64
(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
  • anonymous
ohhh okay okay
anonymous
  • anonymous
wait still confused
anonymous
  • anonymous
so what would be the equation for yz?
Hero
  • Hero
How do I unsubscribe from this?
amistre64
  • amistre64
yz: no-x plane; centers on (y,z) with a radius of: sqrt(5^2 - x^2)
anonymous
  • anonymous
so 25-4? root 21?
amistre64
  • amistre64
yep
amistre64
  • amistre64
and r^2 = 21 then in your equation of circle stuff
anonymous
  • anonymous
but how would i do xz?
anonymous
  • anonymous
r = root(25-36)
amistre64
  • amistre64
well, it centers in the no-y so (x,z); its radius is then sqrt(5^2-y^2)
amistre64
  • amistre64
yep
anonymous
  • anonymous
but its a negative number
amistre64
  • amistre64
it is isnt it :) tell me; if your stretching to reach 5 and your 6 away, do you hit it?
anonymous
  • anonymous
yeah bc r =6?
amistre64
  • amistre64
|dw:1327252967020:dw|
anonymous
  • anonymous
oh so it never intersects?
amistre64
  • amistre64
its negative meaning there is no real radius in that plane so we aint even touching it
anonymous
  • anonymous
so there wouldn't be an equation for xz
amistre64
  • amistre64
correct; the xz plane has no intersection with the sphere
anonymous
  • anonymous
awesome! thank you so much!
amistre64
  • amistre64
yep

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