How to Find the Asymptotes of a Hyperbola


The hyperbola is a conic section. The term hyperbola is referred to the two disconnected curves shown in the to find asymptotes of a hyperbola |

If the principal axes are coinciding with the Cartesian axes, the general equation of hyperbola is of the form:

How to find asymptotes of a hyperbola |

These hyperbolas are symmetric around y axis and are known as y-axis hyperbola. The hyperbola symmetric around x-axis (or x-axis hyperbola) are given by the equation,

How to find asymptotes of a hyperbola | clickspay.ruHow to find the asymptotes of a hyperbola 

To find the asymptotes of a hyperbola, use a simple manipulation of the equation of the parabola.

i. First bring the equation of the parabola to above given form

If the parabola is given as mx2+ny2=l, by defining  

a=√(l/m) and b=√(-l/n) where l<0

(This step is not necessary if the equation is given in standard from.

How to find asymptotes of a hyperbola |

ii. Then, replace the right hand side of the equation with zero.

How to find asymptotes of a hyperbola |

iii. Factorize the equation and take solutions

How to find asymptotes of a hyperbola |

Therefore, the solutions are,

How to find asymptotes of a hyperbola |

Equations of the asymptotes are

How to find asymptotes of a hyperbola |

Equations of the asymptotes for the x-axis hyperbola also can be obtained by the same procedure.

Find the asymptotes of a hyperbola – Example 1

Consider the hyperbola given by the equation x2/4-y2/9=1. Find the equations of the asymptotes.

How to find asymptotes of a hyperbola |

Rewrite the equation and follow the above procedure.
x2/4-y2/9=x2/22 -y2/32 =1

By replacing the right hand side with zero, the equation becomes x2/22 -y2/32 =0.
Factorizing and taking solution of the equation give,


Equations of the asymptotes are,

3x-2y=0 and 3x+2y=0

Find the asymptotes of a hyperbola – Example 2

  • Equation of a parabola is given as -4x² + y² = 4

How to find asymptotes of a hyperbola |

This hyperbola is an x-axis hyperbola.
Rearranging the terms of the hyperbola into the standard from gives
-4x2+ y2= 4=>y2/22 -x2/12 =1
Factorizing the equation provides the following
Therefore, the solutions are y-2x=0 and y+2x=0.

About the Author: admin

Leave a Comment

Related pages

what is difference between wasp and hornetwhat is the difference between shark and whalepolypropylene copolymer vs homopolymerthe difference between thermoplastic and thermosetting plasticdefine deceleration physicsanother word for effecteddifference mandarin cantonesestatic and round charactersferric and ferrousindian flag chakra meaningexplain the difference between race and ethnicitya thermosetting plastichow to find asymptotes of a hyperbolashakespeare comedies and tragedieshow to find asymptotes of a hyperbolaacylatinggeek nerd differencecompressive force definitionirregular heptagonidioms and phrases examplesdifference between relish and chutneystoma guard cellsferrous state of ironexample of macronutrientsdefine condecendgerman vs american rottweilersliteral vs figurative language worksheetsrolling friction physicsdefine micronutrientscereals meaningwhat does amicably meandifference between syllable and morphemehematopoiesis diagramdifference between phd and doctoratefacts about bullmastiffchemical composition of formaldehydedefine soliloquy in literaturehow to find transmittance from absorbancedistinguish between the two different species of rhinocerospermeability vs porosityrules for a cinquain poemnucleolus in nucleusdefinition concrete nounbrandy vs cognac differencerefrain poetry examplesrotational motion meaningsoundwaves radiogerman rotwillertypes of vernier calliperscompare sex chromosomes with autosomesbewilder definitionsingapore airport tax refunddifference between electrical resistance and resistivityalude meaningpast tense of forgocatabolism and anabolism definitionwhat is plumuledefine acid test ratiowhat is the definition of prehistoricexamples of internal rhyme in the ravendiff between plant cell and animal cellchromatin consists ofdefine nocturnal animalshow to derive centripetal accelerationdefinition of retrovirusautotrophs vs heterotrophswhat is the difference between aunt and auntiedifference between poetry and prosedefinition centrosomeschizoaffective disorder schizophreniadifference of brandy and whisky