A latus rectum in conics is a line segment that passes through the focus of a conic section and is perpendicular to the major axis. It is also equal in length to the distance from the focus to the directrix of the conic section.
The length of a latus rectum can be found by using the equation L = 2b²/a, where b is the length of the semi-minor axis and a is the length of the semi-major axis.
The latus rectum is important in conics because it is used to determine the eccentricity of the conic section. It is also used to find the vertex, focus, directrix, and other key points of the conic.
Yes, it is possible to have a negative latus rectum in conics. This occurs when the focus and directrix are on opposite sides of the conic. In this case, the latus rectum is still equal in length to the distance from the focus to the directrix, but it is measured in the opposite direction.
In a parabola, the latus rectum is equal to the diameter of the parabola. In an ellipse, the latus rectum is half the length of the major axis. In a hyperbola, the latus rectum is equal to the distance between the two vertices.