For specifying a straight line, how many geomatrical parameters should be known ?

Options

A. 1
B. 2
C. 4
D. 3

Explanation

To determine how many geometrical parameters are required to specify a straight line, we can analyze different forms of the line's equation and the parameters involved in each form.

### Step-by-Step Solution:

1. **Identify the Forms of the Line**:
- The equation of a straight line can be represented in various forms, such as:
- Slope-Intercept Form: \( y = mx + c \)
- Intercept Form: \( \frac{x}{a} + \frac{y}{b} = 1 \)
- Normal Form: \( x \sin \omega + y \cos \omega = p \)

2. **Analyze the Slope-Intercept Form**:
- In the slope-intercept form \( y = mx + c \):
- \( m \) represents the slope of the line.
- \( c \) represents the y-intercept.
- **Parameters Required**: 2 (m and c)

3. **Analyze the Intercept Form**:
- In the intercept form \( \frac{x}{a} + \frac{y}{b} = 1 \):
- \( a \) is the x-intercept.
- \( b \) is the y-intercept.
- **Parameters Required**: 2 (a and b)

4. **Analyze the Normal Form**:
- In the normal form \( x \sin \omega + y \cos \omega = p \):
- \( \omega \) is the angle made with the x-axis.
- \( p \) is the perpendicular distance from the origin to the line.
- **Parameters Required**: 2 (ω and p)

5. **Conclusion**:
- In all three forms of the line's equation, we find that **2 parameters are required** to uniquely specify a straight line.
- Therefore, the answer is **2**.

### Final Answer:
To specify a straight line, **2 geometrical parameters** should be known.

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