How this calculator works
A latus rectum is a chord through a focus perpendicular to the main axis. Its endpoints lie one half-chord length on either side of that focus. This page finds their actual coordinates, including translations and both focal chords for ellipses and hyperbolas. For a parabola, the quadratic is y = Ax^2+Bx+C when the main axis is vertical and x = Ay^2+By+C when horizontal. Coordinates and axes must share one unit.
Formula
Ellipse or hyperbola: half chord l = b^2/a, full length = 2l. Ellipse c=sqrt(a^2-b^2); hyperbola c=sqrt(a^2+b^2). Parabola p=1/(4A), full length=4|p|.
Worked example
For the ellipse x^2/25 + y^2/9 = 1, c = 4 and each half chord is 9/5 = 1.8. The right focal chord joins (4, -1.8) and (4, 1.8), giving full length 3.6.
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Frequently asked questions
Is this the same as a diameter?
Only for a circle. In a general conic the focal chord is determined by a focus, not the centre.
Can an ellipse have equal semi-axes?
Yes. It becomes a circle, both foci coincide, and the two returned focal chords are the same diameter.
Why specify orientation?
The scalar length is unchanged by rotation through 90 degrees, but the endpoint coordinates change.