What is the asymptotes of (x^2)/(10)-(y^2)/(90)=1 ?

The asymptotes of (x^2)/(10)-(y^2)/(90)=1 is y=3x,\quad y=-3x

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asymptotes of (x^2)/(10)-(y^2)/(90)=1

asymptotes

\frac{x ^{2}}{10} - \frac{y ^{2}}{90} = 1

y = 3 x, y = - 3 x

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{10} - \frac{y ^{2}}{90} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 10, b = 310

y = \frac{3 10}{10} (x - 0) + 0, y = - \frac{3 10}{10} (x - 0) + 0

Refine

y = 3 x, y = - 3 x

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

x^{2} - 3 y^{2} - 2 x - 6 y + 7 = 0

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

10 x^{2} - 25 y^{2} = 100

(x - 4)^{2} - (y + 1)^{2} = 25

What is the asymptotes of (x^2)/(10)-(y^2)/(90)=1 ?
The asymptotes of (x^2)/(10)-(y^2)/(90)=1 is y=3x,\quad y=-3x