Writing the equation of a hyperbola given the foci and vertices

Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola.

The center of the hyperbola is given by (h, k). It is halfway between the two vertices and halfway between the two foci. 'a' is the distance from the center to the vertices and 'b' is the distance from the center to the covertices. 'c' is the distance from the center to the foci. The relationship between a, b and c is a^2 + b^2 = c^2. Using these characteristics of the hyperbola, we can then plug them into the standard equation to obtain the equation of the given hyperbola.

Note that a hyperbola is vertical when it is facing up and down and is horizontal when it is facing right and left. When a hyperbola is vertical, the vertices and the foci are in the y-axis but they are in the x-axis when the hyperbola is horizontal.
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections