The latus rectum of a parabola whose focal chord is PSQ such that SP = 3 and SQ = 2

Options

A. 24/5
B. 43804
C. 43621
D. none of these

Explanation

To find the latus rectum of a parabola given the focal chord PSQ with lengths SP = 3 and SQ = 2, we can use the property of the harmonic mean.

### Step-by-Step Solution:

1. **Identify the lengths of the segments**:
- SP = 3
- SQ = 2

2. **Use the formula for the semi-latus rectum**:
The semi-latus rectum (l) of a parabola can be calculated using the harmonic mean of the segments of the focal chord:
\[ l = \frac{2 \cdot SP \cdot SQ}{SP + SQ} \]

3. **Substitute the values into the formula**:
\[ l = \frac{2 \cdot 3 \cdot 2}{3 + 2} \]

4. **Calculate the denominator**:
\[ SP + SQ = 3 + 2 = 5 \]

5. **Calculate the numerator**:
\[ 2 \cdot 3 \cdot 2 = 12 \]

6. **Combine the results**:
\[ l = \frac{12}{5} \]

7. **Final Result**:
The semi-latus rectum of the parabola is \(\frac{12}{5}\).