find the equation of the right circular cylinder of radius 3 with axis as x-1/2=y-3/2=z-5/-1.
Answers
Answer:
(x - 1/2)^2 + (y - 3/2)^2 = 9
with 0 ≤ z ≤ 5.
Step-by-step explanation:
The axis of the cylinder is given by the equation:
x - 1/2 = y - 3/2 = z + 5/1
We can rewrite this equation in the parametric form as follows:
x = 1/2 + r cos(theta)
y = 3/2 + r sin(theta)
z = -5 + h
where r is the radius of the cylinder, theta is the angle of rotation around the axis, and h is the height of the cylinder.
Since the radius of the cylinder is given as 3, we have r = 3.
To find the height h of the cylinder, we note that the axis passes through the point (1/2, 3/2, -5), which is on the surface of the cylinder. Hence, the height of the cylinder is given by the distance between the point (1/2, 3/2, -5) and the point (1/2, 3/2, 0), which is 5.
(x - 1/2)^2 + (y - 3/2)^2 = 9
with 0 ≤ z ≤ 5.
To know more about right circular cylinder refer :
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