Question

The length of the latus rectum of \(x^2 = -9y\) is equal to:

• A. 3
• B. -3
• C. 9/4
• D. 9

Hint:

For any standard parabola equation, the length of the latus rectum is simply the absolute value of the coefficient of the first-degree variable.
For \(x^2 = -9y\), the coefficient of \(y\) is \(-9\). Taking its absolute value gives 9 instantly.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A parabola is the locus of points that are equidistant from a fixed point (focus) and a fixed line (directrix).
The latus rectum is the line segment passing through the focus, perpendicular to the axis of symmetry, with both endpoints lying on the parabola.

Step 2: Key Formula or Approach:
For any standard parabola of the form \(x^2 = 4ay\) or \(x^2 = -4ay\), the length of the latus rectum is defined as:
\[ \text{Length of Latus Rectum} = 4a \]
This length represents a physical distance, so it is always a positive value.

Step 3: Detailed Explanation:
We are given the equation of the parabola:
\[ x^2 = -9y \]
Let us compare this equation with the standard downward-opening parabola form:
\[ x^2 = -4ay \]
By comparing the coefficients of \(y\) on both sides:
\[ -4a = -9 \implies 4a = 9 \]
The term \(4a\) represents the length of the latus rectum of the parabola.
Therefore, the length of the latus rectum is exactly 9.
This matches the fourth option.

Step 4: Final Answer:
Therefore, the correct option is (D).