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What is the formula for finding the asymptote of hyperbola?

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Learn Hyperbola +2 Class XI-XII Tuition (PUC) Mathematics

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

y -- 2 = ± (3/4)(x + 3).
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y = +-(b/a)*x for x^2/a^2 + y^2/b^2 = 1.
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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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It is a line such that the distance between the curve and the line approaches zero as they tend to infinity.an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity.
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Y-a = 4K (X-b)^2.
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What is the equation of rectangular hyperbola?
x2 - y2 = a2 equation of rectangular hyperbola.
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