Difference between revisions of "Math 22 The Three-Dimensional Coordinate System"
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<math>(x-h)^2+(y-k)^2+(z-j)^2=r^2</math> | <math>(x-h)^2+(y-k)^2+(z-j)^2=r^2</math> | ||
+ | |||
+ | '''Exercises 3''' Find the equation of the sphere that has: | ||
+ | |||
+ | '''1)''' Center: <math>(1,2,0)</math> and radius: <math>5</math> | ||
+ | {| class = "mw-collapsible mw-collapsed" style = "text-align:left;" | ||
+ | !Solution: | ||
+ | |- | ||
+ | |<math>(x-h)^2+(y-k)^2+(z-j)^2=r^2</math> | ||
+ | |- | ||
+ | |So, <math>(x-1)^2+(y-2)^2+(z-0)^2=5^2</math> | ||
+ | |- | ||
+ | |Therefore, <math>(x-1)^2+(y-2)^2+z^2=25 | ||
+ | |} | ||
+ | |||
+ | '''2)''' Center: <math>(-1,2,4)</math> and radius: <math>2</math> | ||
+ | {| class = "mw-collapsible mw-collapsed" style = "text-align:left;" | ||
+ | !Solution: | ||
+ | |- | ||
+ | |<math>(x-h)^2+(y-k)^2+(z-j)^2=r^2</math> | ||
+ | |- | ||
+ | |So, <math>(x-(-1))^2+(y-2)^2+(z-4)^2=2^2</math> | ||
+ | |- | ||
+ | |Therefore, <math>(x+1)^2+(y-2)^2+(z-4)^2=4 | ||
+ | |} | ||
[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' |
Revision as of 07:42, 18 August 2020
The Three-Dimensional Coordinate System
The Distance and Midpoint Formulas
The distance between the points and is
Exercises 1 Find the distance between two points
1) and
Solution: |
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2) and
Solution: |
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Midpoint Formula in Space
The midpoint of the line segment joining the points and is
Exercises 2 Find the midpoint of two points below:
1) and
Solution: |
---|
2) and
Solution: |
---|
Standard Equation of a Sphere
The standard equation of a sphere with center at and radius is:
Exercises 3 Find the equation of the sphere that has:
1) Center: and radius:
Solution: | ||||
---|---|---|---|---|
So, | ||||
Therefore, Failed to parse (syntax error): {\displaystyle (x-1)^2+(y-2)^2+z^2=25 |} '''2)''' Center: <math>(-1,2,4)}
and radius:
This page were made by Tri Phan |