The plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle `alpha`. Prove that the equation of the plane in its new position is ` ax + by +- (sqrt(a^2 + b^2) tan alpha)z = 0`

Explanation

To solve the problem, we need to find the equation of the plane after it has been rotated about its line of intersection with the plane \( z = 0 \) through an angle \( \alpha \).

### Step-by-Step Solution:

1. **Identify the Given Planes**:
- The first plane is given by the equation \( P_1: ax + by = 0 \).
- The second plane is the horizontal plane \( P_2: z = 0 \).

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