Math July 13, 2026 · 8 Min Read

Latus Rectum Calculator – Guide & Formulas

Calculate the latus rectum of a parabola or hyperbola instantly. Free online tool with step-by-step solutions using standard and vertex form equations.

Calculate the latus rectum of any parabola or hyperbola instantly. Enter the equation parameters to get the latus rectum length, focus coordinates, and step-by-step solutions.

Key Takeaway

Use the free Latus Rectum Calculator to calculate the latus rectum of a parabola or hyperbola instantly. free online tool with step-by-step solutions using standard and vertex form equations. Get instant results with step-by-step explanations.

How to Use the Latus Rectum Calculator

  1. Select the conic section type: Parabola or Hyperbola.
  2. Choose the equation form (standard or vertex form).
  3. Enter the coefficients and constants from your equation.
  4. Review the latus rectum length, focus coordinates, and directrix information.

The Formula

Parabola: LR = 4|p|, where p is the distance from vertex to focus. Hyperbola: LR = 2b²/a, where a and b are the semi-major and semi-minor axes.

Variable Definitions

  • p: Distance from the vertex to the focus of a parabola
  • a: Semi-major axis length (half the transverse axis) for a hyperbola
  • b: Semi-minor axis length (half the conjugate axis) for a hyperbola
  • LR: Length of the latus rectum (focal chord perpendicular to the axis)

Latus Rectum of y² = 12x

Find the latus rectum for a parabola in standard form.

  1. Step 1: Identify the form: y² = 4px, so 4p = 12.
  2. Step 2: Solve for p: p = 12/4 = 3.
  3. Step 3: Latus rectum length = 4|p| = 4 × 3 = 12.
  4. Step 4: Focus is at (p, 0) = (3, 0), directrix is x = -3.

Frequently Asked Questions

What is the latus rectum?

The latus rectum is a line segment passing through the focus of a conic section (parabola, ellipse, or hyperbola) that is perpendicular to the axis of symmetry. Its length is a key property of the conic.

How do I find p from y² = 4px?

Compare your equation to the standard form y² = 4px. The coefficient of x equals 4p, so p = (coefficient of x) / 4. For example, y² = 12x gives p = 3.

What is the latus rectum of a circle?

A circle is a special case of an ellipse where a = b = r (radius). The latus rectum of a circle has length 2r, which is the diameter through the focus (center).

Does the latus rectum direction matter?

Yes. For parabolas opening right/left (y² = 4px), the latus rectum is vertical. For parabolas opening up/down (x² = 4py), the latus rectum is horizontal. The length is the same regardless.

How is the latus rectum different from the major axis?

The major axis passes through the center and both vertices of an ellipse/hyperbola. The latus rectum passes through the focus perpendicular to the axis. They are perpendicular to each other.

Can I use this for ellipses?

Yes, the same principle applies. For an ellipse x²/a² + y²/b² = 1, the latus rectum through each focus has length 2b²/a.

What if my equation is in vertex form?

For parabolas: (y-k)² = 4p(x-h) or (x-h)² = 4p(y-k). The latus rectum length is still 4|p|, regardless of the vertex position (h,k).

How does the latus rectum relate to the focal parameter?

The focal parameter (semi-latus rectum) is half the latus rectum. For a parabola, the semi-latus rectum equals |2p|. It determines the "width" of the conic at the focus.