The **length of the latus rectum** of a parabola is a line segment perpendicular to the axis of symmetry that passes through the focus, with its endpoints on the parabola.

For a parabola in the form \( y^2 = 4px \), the length of the latus rectum is given by the absolute value of \( 4p \).

### Given Equation:
\[
y^2 = 20x
\]

### Comparison with Standard Form:
The equation \( y^2 = 20x \) is in the standard form \( y^2 = 4px \).

From this, we identify:
\[
4p = 20
\]

So, the value of \( p \) is:
\[
p = \frac{20}{4} = 5
\]

### Length of the Latus Rectum:
The length of the latus rectum is \( |4p| \):
\[
\text{Length of the Latus Rectum} = |4p| = 20
\]

### Final Answer:
The length of the latus rectum for the parabola \( y^2 = 20x \) is **20 units**.

Would you like to explore any more details or have any further questions?

### Follow-up Questions:
1. How would the length of the latus rectum change if the equation were \( y^2 = 8x \)?
2. Can you derive the latus rectum length for a parabola that opens vertically, such as \( x^2 = 12y \)?
3. How does the latus rectum relate to the area of the parabola segment?
4. What is the significance of the latus rectum in determining the shape of the parabola?
5. How would you graph the latus rectum on the coordinate plane for this parabola?

### Tip:
Remember that the length of the latus rectum is always a positive value, as it represents a physical distance on the graph.

Learn how to find the length of the latus rectum for the parabola y^2 = 20x. This problem involves understanding parabolas, their standard form, and calculating the length of the latus rectum using the formula |4p|. Suitable for high school students.

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