Hyperbola Equation Calculator: Find Standard Form

Understanding Hyperbola Equations

A hyperbola is a type of conic section defined as the locus of points such that the difference of the distances from two fixed points, called foci, is constant. The standard form of a hyperbola centered at (h, k) depends on its orientation:

• Horizontal Hyperbola: $$ \frac{(x - h) ^ 2}{a ^ 2} - \frac{(y - k) ^ 2}{b ^ 2} = 1 $$
• Vertical Hyperbola: $$ \frac{(y - k) ^ 2}{a ^ 2} - \frac{(x - h) ^ 2}{b ^ 2} = 1 $$

Here, (h, k) is the center, \'a\' is the semi-transverse axis, and \'b\' is the semi-conjugate axis. The distance from the center to each focus is \'c\', where $$c^2 = a^2 + b^2$$. The transverse axis length is 2a, which is the constant difference of distances from any point on the hyperbola to the two foci.

Use this calculator to quickly find the equation of a hyperbola and visualize its shape based on the given foci and transverse axis length.