AP Calculus BC › 3-Dimensional Space
Find an equation of a sphere that has the line segment joining (0,4,2) and (6,0,2) as a diameter.
None of the Above.
To find the diameter we need to find the distance between the two points, where:
So
Since the radius is half of the Diameter,
To find the the Center point we use the mid-point formula. So,
So the equation of the sphere is:
a
Express the three-dimensional (x,y,z) Cartesian coordinates as cylindrical coordinates (r, θ, z):
The coordinates (2, 1, -2) corresponds to: x = 2, y = 1, z = -2, and are to be converted to the cylindrical coordinates in form of (r, θ, z), where:
So, filling in for x, y, z:
Then the cylindrical coordinates are represented as: