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  Hyperbola Homework Help - K-12 Grade Level, College Level Geometry Mathematics

Introduction of Hyperbola

A Hyperbola is a type of smooth curve lying in a plane, described by its geometric properties or by equations for which it is the solution set. It has two pieces, called connected components or branches that are mirror images of each other and resemble two infinite bows. It is one of the four kinds of conic section that is formed by the intersection of a plane and a cone. The other conic sections are the ellipse, parabola and circle (the circle is a special case of the ellipse). Which conic section is formed is depends on the angle the plane makes with the axis of the cone compared with the angle a straight line on the surface of the cone makes with the axis of the cone. If the angle, that is between the plane and the axis is less than the angle between the line on the cone and the axis or if the plane is parallel to the axis, then the plane intersects both the conic is a hyperbola and halves of the double cone.

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General form of a hyperbola

You can state all conics as a second degree equation. This equation is recognized as the general form of conics.

ax2 + by2 + 2gx + 2fy + c this is general form of all conics

You can classify the type of conic by comparing values of a and b.

If ab < 0, then This will form a hyperbola.  In other words, a and b should have been a opposite signs.

When a < 0 &  b > 0, the hyperbola opens up or down. When a > 0 and b < 0, the hyperbola opens right or left.

The general form of the equation of a hyperbola which is horizontally aligned

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(h,k) is known as center of the horizontally aligned hyperbola.

a is the distance from the center of the hyperbola to each vertex of the hyperbola.

Each and every vertex of the hyperbola lies on the transverse axis of the hyperbola and transverse axis of a horizontally aligned hyperbola is horizontal.

The general form of the hyperbola equation which is a vertically aligned is: 

 

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