What is the asymptotes of 4y^2-9x^2+16y+18x=29 ?

The asymptotes of 4y^2-9x^2+16y+18x=29 is y= 3/2 (x-1)-2,\quad y=-3/2 (x-1)-2

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asymptotes of 4y^2-9x^2+16y+18x=29

asymptotes

4 y^{2} - 9 x^{2} + 16 y + 18 x = 29

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

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - 9 x^{2} + 16 y + 18 x = 29 :

Up-down Hyperbola with

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

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

y^{2} - 25 x^{2} = 25

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{5} = 1

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1

y^{2} - x^{2} = 16

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

What is the asymptotes of 4y^2-9x^2+16y+18x=29 ?
The asymptotes of 4y^2-9x^2+16y+18x=29 is y= 3/2 (x-1)-2,\quad y=-3/2 (x-1)-2