Question

Use complete sentences to describe how a hyperbola is defined in terms of distances.

Answer 1

Hyperbola:

A hyperbola is locus of all the points,in a plane ,such that, if you take a single point among all those points ,and find the distance from two fixed points called  foci, and get the modulus of difference of those two distances ,it gives a constant value.

Let us consider the set of all those points by (x,y).

And foci on two sides of X axis is represented  by F(p,0) and F'(-p,0).

This line is called Major Axis.

$\sqrt{(x-p)^2+(y-0)^2}- \sqrt{(x+p)^2+(y-0)^2}=\pm 2s$

Where, (s,0) and (-s,0) are the coordinates of two vertices of hyperbola.

Answer 2

Hyperbola is the set of all points in a plane such that the difference of the distances from two fixed points (foci) is constant.