The center of a hyperbola is located at (0, 0). One focus is located at (0, 5) and its associated directrix is represented by the line y = . Given the standard form of the equation of a hyperbola, what are the values of a and b?
In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of .:2a
2a is used in the equation because the is a point on the hyperbola and it is the difference in the distances from this point to the foci.:vertex
This can be shown algebraically if we let a be the distance from the to the vertex. Then, the difference of the distances is (c + a) – .:center
This can be shown algebraically if we let a be the distance from the to the vertex. Then, the difference of the distances is (c + a) – .:(c – a)