Find The Latus Rectum Calculator

Latus Rectum Equation:

\[ \text{Latus Rectum} = 4a \text{ (for parabola)} \] \[ \text{Latus Rectum} = \frac{2b^2}{a} \text{ (for ellipse)} \] \[ \text{Latus Rectum} = \frac{2b^2}{a} \text{ (for hyperbola)} \]

Latus Rectum:

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1. What is the Latus Rectum?

The latus rectum is a line segment perpendicular to the axis of symmetry of a conic section (parabola, ellipse, or hyperbola) that passes through the focus and whose endpoints lie on the curve.

2. How Does the Calculator Work?

The calculator uses different equations based on the conic section type:

For parabola: \[ \text{Latus Rectum} = 4a \]

For ellipse: \[ \text{Latus Rectum} = \frac{2b^2}{a} \]

For hyperbola: \[ \text{Latus Rectum} = \frac{2b^2}{a} \]

Where:

\( a \) — Major axis parameter
\( b \) — Minor axis parameter (for ellipse/hyperbola)

3. Importance of Latus Rectum

Details: The latus rectum helps characterize the shape and properties of conic sections. It's particularly important in optics and orbital mechanics applications.

4. Using the Calculator

Tips: Select the conic section type, enter the value of 'a', and for ellipses/hyperbolas, enter the value of 'b'. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between latus rectum for different conic sections?
A: For parabolas, it's simply 4a. For ellipses and hyperbolas, it depends on both a and b parameters.

Q2: Can latus rectum be negative?
A: No, since it represents a length, it's always positive when defined.

Q3: What are typical values for a and b?
A: These depend on the specific conic section. For standard forms, they're usually positive real numbers.

Q4: How does latus rectum relate to focus?
A: The latus rectum passes through the focus and is perpendicular to the major axis.

Q5: Why is it called "latus rectum"?
A: The term comes from Latin, meaning "straight side," referring to its geometric properties.