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What is the formula for finding the asymptote of hyperbola?

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CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Hyperbola

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y-k =+/- b/a( x-h).

If you take standard hyperbola as: X^2/a^2- y^2/b^2 =1 the consider x^2/a^2 - y^2/b^2 = 0 Which gives (x/a - y/b) (x/a+y/b) = 0 Solve it to get separate equations.


Use this standard form of equation x2 (x square )/a2 (a square) - y2 (y square)/b2 (b square) = 1.


(x - 3)2/4 - (y + 1)2/25 = 1. Set this equal to 0 and factor to get:- ((x - 3)/2 + (y + 1)/5)((x - 3)/2 - (y + 1)/5) = 0. Separate each factor and solve to find the equations of the asymptotes:- (x - 3)/2 + (y + 1)/5 = 0 ? y = -5/2x + 13/2 ((x - 3)/2 - (y + 1)/5) = 0 ? y = 5/2x - 17/2.

Let me tell you in step wise:- step 1 : Write down the equation of the hyperbola in standard form. step 2 : Set the equation equal to zero instead of one. step 3 : Factor the new equation. step 4 : Separate the factors and solve for y Try it for difficult sums also. Hope you will understand .

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y = +/- (b/a)(x - h) + k.


y -- 2 = (3/4)(x + 3).


y = +-(b/a)*x for x^2/a^2 + y^2/b^2 = 1.


Asymptotes of a hyperbola are the lines that pass through center of the hyperbola. The formula is y=+or- (b/a)x.

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There is no particular formula for finding asymptote of hyperbola. But there is a condition i.e., asymptote equation and hyperbola equations are differ by constant.

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