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The problem asks for the equation of a parabola in standard form, given that it is centered at the origin, has a latus rectum length of 10, and opens to the left.

### Steps to Solve:
1. **Understanding the Latus Rectum**: For a parabola, the length of the latus rectum \( |4p| \) is given. Here, \( |4p| = 10 \), so \( p = \frac{10}{4} = \frac{5}{2} \).

2. **Direction of Opening**: Since the parabola opens to the left, the standard form of the equation is \( y^2 = -4px \).

3. **Substituting the Value of \( p \)**: Substituting \( p = \frac{5}{2} \) into the equation:
   \[
   y^2 = -4\left(\frac{5}{2}\right)x = -10x
   \]

### Answer:
The correct equation is \( y^2 = -10x \).

Would you like more details, or have any other questions?

### Relative Questions:
1. How does the latus rectum relate to the focus of a parabola?
2. What is the effect of changing the value of \( p \) on the shape of the parabola?
3. Can you explain why the sign of \( p \) determines the direction of the parabola's opening?
4. How would the equation change if the parabola opened to the right instead?
5. What are the differences between the standard forms of vertical and horizontal parabolas?

### Tip:
When dealing with parabolas, always check the direction it opens to ensure the correct sign in the equation.

What is the equation of the parabola in standard form with vertex at its origin, the length of the latus rectum is 10, and the parabola opens to the left?

Solve the equation of a parabola with a latus rectum length of 10 and opening to the left. Learn the relationship between latus rectum and p in the equation y^2 = -10x.

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