If have vertex of a parabola be at origin and directrix be `x + 5 =0,` then its latus pectum is

Options

A. 5
B. 10
C. 20
D. 40

Answer

To solve the problem step by step, we need to find the length of the latus rectum of a parabola given its vertex and directrix.

### Step-by-Step Solution:

1. **Identify the Vertex and Directrix:**
- The vertex of the parabola is given as the origin (0, 0).
- The directrix is given by the equation \( x + 5 = 0 \), which simplifies to \( x = -5 \).

2. **Determine the Orientation of the Parabola:**
- Since the vertex is at the origin and the directrix is a vertical line (x = -5), the parabola opens to the right.

3. **Find the Value of 'a':**
- The distance from the vertex to the directrix is equal to 'a'.
- The vertex is at (0, 0) and the directrix is at \( x = -5 \).
- The distance from the vertex to the directrix is:
\[ |0 - (-5)| = 5 \]
- Therefore, \( a = 5 \).

4. **Calculate the Length of the Latus Rectum:**
- The length of the latus rectum of a parabola is given by the formula:
\[ \text{Length of Latus Rectum} = 4a \]
- Substituting the value of 'a':
\[ \text{Length of Latus Rectum} = 4 \times 5 = 20 \]

5. **Final Answer:**
- The length of the latus rectum is \( 20 \).