## The Foci of a Hyperbola

The foci of a hyperbola are two points on the hyperbola that are equidistant from the centre. The vertices of a hyperbola are the points on the hyperbola where the two legs of the hyperbola intersect. The equation of the hyperbola with foci (5,0) and (5,0) and vertices (4,0) and (4,0) is given by:

### The foci of a hyperbola are the two points that lie on the major axis and are equidistant from the center of the hyperbola.

A hyperbola is a type of curve that looks like two disconnected parts of a parabola. It is defined by the set of points in a plane that are equidistant from two fixed points (the foci) and a given line (the directrix).

### The vertices of a hyperbola are the two points that lie on the minor axis and are equidistant from the center of the hyperbola.

A hyperbola is a type of conic section that has two points, called foci (pronounced “FOE-sigh”), that lie on its major axis. The vertices of a hyperbola are the two points that lie on the minor axis and are equidistant from the center of the hyperbola. The equation of a hyperbola with foci at (5, 0) and (5, 0) and vertices at (4, 0) and (4, 0) is given by the equation:

(x-5)^2-(y-0)^2=25

This equation can be rewritten in standard form as follows:

(x^2-10x+25)-(y^2-0)=0

Which can be further simplified to:

x^2-10x+25-y^2=0

## The Equation of a Hyperbola

A hyperbola is a type of curve that is defined by two points (the foci) and two line segments (the vertices). The equation of a hyperbola can be written in standard form or in general form. The standard form equation of a hyperbola is: (x-h)^2/a^2-(y-k)^2/b^2=1. The equation of a hyperbola in general form is: Ax^2+Bxy+Cy^2+Dx+Ey+F=0.

### The equation of a hyperbola with foci at (5, 0) and (5, 0) and vertices at (4, 0) and (4, 0) is (x – 5)^2/25 – (y – 0)^2/16 = 1.

A hyperbola is a curve with two branches, each of which is the graph of a equation in the form (x-h)^2/a^2-(y-k)^2/b^2=1 where a and b are positive real numbers and a does not equal b. The point (h, k) is the center of the hyperbola. The vertices of the hyperbola are the points (h+a, k) and (h-a, k). The foci of the hyperbola are the points (h+c, k) and (h-c, k), where c^2=a^2+b^2.