liamnerf said:Hello. I am currently trying to calculate the equation of a hyperbola, which I have little experience with. The hyperbola has a "sphere radius" of 153mm and a "hyperbolic factor" of 21500. I haven't been able to find anything online about what these mean and am lost. The parameters where given to me by a program called optical ray tracer which is used to model light rays in 2D. I am currently designing a telescope's mirror.
To find the center of a hyperbola, you will need to know the coordinates of the vertices and the foci. The center of a hyperbola is located at the midpoint between the two vertices.
The standard form of a hyperbola's equation is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola and a and b are the distances from the center to the vertices and foci respectively.
The eccentricity of a hyperbola can be calculated using the formula e = c/a, where c is the distance from the center to the focus and a is the distance from the center to the vertex. The eccentricity of a hyperbola is always greater than 1.
No, you will need at least two points on the curve to determine the equation of a hyperbola. This is because a hyperbola has two branches and one point alone cannot determine the shape of the entire curve.
A horizontal hyperbola has its transverse axis (the line connecting the two vertices) running horizontally, while a vertical hyperbola has its transverse axis running vertically. This difference affects the values of a and b in the standard form of the equation, but does not change the overall shape of the hyperbola.