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The radius of the circle in which the...

The radius of the circle in which the sphere `x^(2)+y^2+z^2+2z-2y-4z-19=0` is cut by the plane `x+2y+2z+7=0` is a. `2` b. `3` c. `4` d. `1`

A

2

B

3

C

4

D

1

Text Solution

AI Generated Solution

To find the radius of the circle formed by the intersection of the sphere and the plane, we will follow these steps: ### Step 1: Rewrite the equation of the sphere The given equation of the sphere is: \[ x^2 + y^2 + z^2 + 2z - 2y - 19 = 0 \] We can rearrange this equation by completing the square for \(x\), \(y\), and \(z\). ...
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