Hyperbola

posted on: 24 May, 2012 | updated on: 23 Aug, 2012

Hyperbola definition states that a line which has curve shape is known as Hyperbola or we can say that both focus (a fix Point) and directrix are always in the same ratio. It is just like a conic section. Conic section looks like a cone shape or a curve which has two branches which are obtained by the Intersection of plane and has both halves just like a Right Circular Cone. When we talk about the difference of distances from the given point then we find that distance is constant.
Now we will define hyperbola in detail:
For drawing the hyperbola in Math we have to follow some steps which are given below:
Step 1: First we take a Line Segment.
Step 2: Then we draw perpendicular to the Line Segment.
Step 3: Then we draw a focal point.
Step 4: If we want vertex then bisect the distance which is measured between line and focal point.
Step 5: Then we plot vertical lines of any distance and name the line as P, Q, R, S, T.
Step 6: Then we measure the distance from line segment to the point ‘P’.
Step 7: Then we measure the distance from line segment to the point ‘Q’ and repeat the same procedure till the last point.
Step 8: We draw the point from the line segment.
Step 9: At last we join all the points and we get hyperbola.
We have two curves which are not connected and these disconnected curves are known as arms or branches of hyperbola. The points of two disconnected curves are known as vertices of hyperbola, and the line which connects both curves is known as transverse axis or major axis of hyperbola.
When the transverse axis of the given hyperbola is aligned with the x – axis then the Equation of Hyperbola is:

⇒ x² - y² = 1;
P² q²
This is equation of hyperbola.

Topics Covered in Hyperbola

Equation of Hyperbola

posted on: 25 Jun, 2012 | updated on: 19 Jul, 2012

Hyperbola in daily life can be seen in the form of a decoration or design. It is a smooth curve and an unbounded case of the conic section, formed by the Intersection of a plane with both halves of a double cone.

The shape of a Hyperbola is well-defined by its eccentricity e, which is a dimensionless number always greater than one. A hyperbola can also be d...Read More

Hyperbola foci

posted on: 18 Jul, 2012 | updated on: 19 Jul, 2012

Hyperbolas are a type of conic sections. They seem to be two parabolas adjusted adjacent to each other when graphed. Hyperbola has two foci. A Hyperbola can be defined as a Set of points such that their distances from the two hyperbola foci maintain a constant difference. This is the reason for two mirror images. Hyperbola finds its applications in various fields like des...Read More

Eccentricity of Hyperbola

posted on: 21 Aug, 2012 | updated on: 22 Aug, 2012

Hyperbola is a Graphical representation of function which relates two or more variables in the following way Y = K X² or X = K Y². Hyperbola is a graph that seems a Combination of two graphs that is one curve with a mirror image. Hyperbola is a graph that contains that Point whose distance is constant from a fixed point. Fixed point is also called as focus and ...Read More

Asymptotes of Hyperbola

posted on: 22 Aug, 2012 | updated on: 23 Aug, 2012

Asymptote can be defined as a straight line that approaches the curve at infinity. That is the distance between the line and curve approaches zero as curve tends to infinity. Asymptote seems to touch the curve but actually it doesn’t. Asymptotes of Hyperbola can be defined as lines which touch the hyperbola at infinity and pass through the center of hyperbola. As...Read More

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