What is the asymptotes of ((x-3)/4)^2-((y-1)/3)^2=1 ?

The asymptotes of ((x-3)/4)^2-((y-1)/3)^2=1 is y= 3/4 (x-3)+1,\quad y=-3/4 (x-3)+1

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asymptotes of ((x-3)/4)^2-((y-1)/3)^2=1

asymptotes

(\frac{x - 3}{4})^{2} - (\frac{y - 1}{3})^{2} = 1

y = \frac{3}{4} (x - 3) + 1, y = - \frac{3}{4} (x - 3) + 1

Solution steps

y = \pm \frac{b}{a} (x - h) + k

Calculate Hyperbola properties

(\frac{x - 3}{4})^{2} - (\frac{y - 1}{3})^{2} = 1 :

Right-left Hyperbola with

(h, k) = (3, 1), a = 4, b = 3

y = \frac{3}{4} (x - 3) + 1, y = - \frac{3}{4} (x - 3) + 1

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0

\frac{y ^{2}}{49} - \frac{x ^{2}}{64} = 1

25 x^{2} - 16 y^{2} + 50 x - 32 y - 391 = 0

\frac{( y ) ^{2}}{12} - \frac{x ^{2}}{16} = 1

What is the asymptotes of ((x-3)/4)^2-((y-1)/3)^2=1 ?
The asymptotes of ((x-3)/4)^2-((y-1)/3)^2=1 is y= 3/4 (x-3)+1,\quad y=-3/4 (x-3)+1