The number of parabolas that can be drawn , if two ends of the latus rectum are given, is

Options

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

Answer

To determine the number of parabolas that can be drawn when the two ends of the latus rectum are given, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Latus Rectum**:
The latus rectum of a parabola is a line segment that passes through the focus of the parabola and is perpendicular to the axis of symmetry. The ends of the latus rectum are points on this segment.

2. **Identifying the Given Points**:
Let the two ends of the latus rectum be denoted as points \( L \) and \( L' \). These points are fixed in space and represent the endpoints of the latus rectum.

3. **Drawing the First Parabola**:
We can draw a parabola that opens towards the focus located between the points \( L \) and \( L' \). This parabola will touch both points \( L \) and \( L' \).

4. **Drawing the Second Parabola**:
We can also draw another parabola that opens in the opposite direction (away from the focus). This parabola will also touch the points \( L \) and \( L' \).

5. **Conclusion on Number of Parabolas**:
Since we can only draw two distinct parabolas (one opening towards the focus and one opening away from it) that touch the two given points \( L \) and \( L' \), we conclude that the total number of parabolas that can be drawn is **2**.

### Final Answer:
The number of parabolas that can be drawn if two ends of the latus rectum are given is **2**.

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