How to find the asymptotes of a hyperbola

hyperbole

The hyperbola is a conic section. The term hyperbola refers to the two separate curves shown in the figure. how to find asymptotes of a hyperbola | euresisjournal.org

When the principal axes coincide with the Cartesian axes, the general hyperbolic equation is of the form:

How to find asymptotes of a hyperbola | euresisjournal.org

These hyperbolas are symmetrical about the y-axis and are referred to as y-axis hyperbolas. The hyperbola symmetrical about the x-axis (or x-axis hyperbola) is given by the equation:

How to find asymptotes of a hyperbola | euresisjournal.org How to find the asymptotes of a hyperbola

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

I. First, bring the equation of the parabola into the above form

If the parabola is given as mx 2 + ny 2 = l , one defines

a = √ ( l / m ) and b = √ ( -l / n ) where l <0

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

How to find asymptotes of a hyperbola | euresisjournal.org

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

How to find asymptotes of a hyperbola | euresisjournal.org

iii. Factor the equation and take solutions

How to find asymptotes of a hyperbola | euresisjournal.org

Hence the solutions

How to find asymptotes of a hyperbola | euresisjournal.org

Are equations of the asymptotes

How to find asymptotes of a hyperbola | euresisjournal.org

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

Find the asymptotes of a hyperbola - Example 1

Consider the hyperbola represented by the equation x 2/4-y 2/9 = 1 is given. Find the equations of the asymptotes.

How to find asymptotes of a hyperbola | euresisjournal.org

Rewrite the equation and follow the above procedure. x 2/4-y 2/9 = x 2/2 2 -y 2/3 2 = 1

By replacing the right hand side with zero, the equation becomes x 2/2 2 -y 2/3 2 = 0. Factoring and solving the equation give

(x / 2-y / 3) (x / 2 + y / 3) = 0

Are equations of the asymptotes,

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

Find the asymptotes of a hyperbola - example 2

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

How to find asymptotes of a hyperbola | euresisjournal.org

This hyperbola is an x-axis hyperbola. The rearranging the terms y of the hyperbola in the standard of result-4x 2 + y 2 = 4 => 2/2 2 -x 2/1 2 = 1 The factorization of the equation yields the following (y / 2-x) (y / 2 + x) = 0 Hence the solutions y-2x = 0 and y + 2x = 0.

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