What is the asymptotes of 9(x-1)^2-16(y+2)^2=144 ?

The asymptotes of 9(x-1)^2-16(y+2)^2=144 is y= 3/4 (x-1)-2,\quad y=-3/4 (x-1)-2

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asymptotes of 9(x-1)^2-16(y+2)^2=144

asymptotes

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144

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

Solution steps

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

Calculate Hyperbola properties

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144 :

Right-left Hyperbola with

(h, k) = (1, - 2), a = 4, b = 3

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

9 x^{2} - y^{2} + 6 y - 18 = 0

4 x^{2} - y^{2} - 24 x - 6 y + 23 = 0

y^{2} - x^{2} = \frac{4}{25}

3 x^{2} - y^{2} + 6 x - 2 y = 10

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 6 ) ^{2}}{4} = 1

What is the asymptotes of 9(x-1)^2-16(y+2)^2=144 ?
The asymptotes of 9(x-1)^2-16(y+2)^2=144 is y= 3/4 (x-1)-2,\quad y=-3/4 (x-1)-2