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 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.
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) – ___.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

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 Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.

This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).

More about the hyperbola link is given below.

https://brainly.com/question/12919612

#SPJ2