Find the equation of Cylindrical surface:Central axis is (x-1)/1=(y+1)/(-2)=(z+3)/(-2) and passing through (1,-2,1);
时间: 2024-06-05 11:09:45 浏览: 15
We can find the equation of the cylindrical surface by using the formula:
(x - a)^2 + (y - b)^2 = r^2
where (a, b) is the center of the circular base and r is the radius of the cylinder.
First, we need to find the center of the circular base. The given central axis is:
(x - 1)/1 = (y + 1)/(-2) = (z + 3)/(-2)
This can be written as:
x - 1 = -2(y + 1)/1 = -2(z + 3)/1
Simplifying, we get:
x = -2y - 1 = -2z - 3
Substituting x = 1, y = -2, and z = 1, we get:
1 = -2(-2) - 1 = -2(1) - 3
Therefore, the center of the circular base is (1, -1, -2).
Next, we need to find the radius of the cylinder. We can do this by finding the distance between the center of the circular base and the given point on the surface, which is (1, -2, 1). Using the distance formula, we get:
r = sqrt((1 - 1)^2 + (-2 + 1)^2 + (1 + 2)^2) = sqrt(6)
Therefore, the equation of the cylindrical surface is:
(x - 1)^2 + (y + 1)^2 = 6
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