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The question asks you to determine the equation of a parabola based on the given conditions:

- The length of the latus rectum is 10.
- The parabola opens to the left.

### Step-by-Step Explanation:
1. **Parabola opening to the left**: When a parabola opens to the left, its equation is of the form \( y^2 = -4px \), where \( p \) is the distance from the vertex to the focus.

2. **Latus rectum**: The length of the latus rectum of a parabola is given by \( |4p| \). Here, the latus rectum is provided as 10, so:
   \[
   |4p| = 10
   \]
   Solving for \( p \):
   \[
   4p = 10 \quad \text{or} \quad 4p = -10 \quad \Rightarrow \quad p = \frac{10}{4} = 2.5
   \]

3. **Equation of the parabola**: Since the parabola opens to the left, \( p \) will be negative. Thus, the equation becomes:
   \[
   y^2 = -4px = -4(2.5)x = -10x
   \]
   
Therefore, the correct equation is \( y^2 = -10x \), which corresponds to the third option.

### Would you like further details on any part of this explanation?

#### Related questions:
1. How do you calculate the latus rectum of a parabola?
2. What are the different forms of a parabola equation based on its orientation?
3. How do you find the vertex and focus of a parabola?
4. What is the significance of the parameter \( p \) in a parabola's equation?
5. How do transformations affect the equation of a parabola?

#### Tip:
When determining the direction a parabola opens, focus on the sign and placement of the variable in the equation (positive for right or upwards, negative for left or downwards).

The length of the latus rectum is 10 and the parabola opens to the left. Find the equation of the parabola.

Learn how to determine the equation of a parabola that opens to the left with a given latus rectum of 10. This problem covers key concepts in conic sections and is suitable for students in Grades 10-12.

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