What is the asymptotes of 3x^2-15y^2+2x-3y=4 ?

The asymptotes of 3x^2-15y^2+2x-3y=4 is y=(3x+1)/(3sqrt(5))-1/10 ,\quad y=-(3x+1)/(3sqrt(5))-1/10

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asymptotes of 3x^2-15y^2+2x-3y=4

asymptotes

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4

y = \frac{3 x + 1}{3 5} - \frac{1}{10}, y = - \frac{3 x + 1}{3 5} - \frac{1}{10}

Solution steps

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

Calculate Hyperbola properties

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4 :

Right-left Hyperbola with

(h, k) = (- \frac{1}{3}, - \frac{1}{10}), a = \frac{251}{6 5}, b = \frac{251}{30}

y = \frac{\frac{251}{30}}{\frac{251}{6 5}} (x - (- \frac{1}{3})) + (- \frac{1}{10}), y = - \frac{\frac{251}{30}}{\frac{251}{6 5}} (x - (- \frac{1}{3})) + (- \frac{1}{10})

Refine

y = \frac{3 x + 1}{3 5} - \frac{1}{10}, y = - \frac{3 x + 1}{3 5} - \frac{1}{10}

25 x^{2} - 9 y^{2} = 225

\frac{y ^{2}}{36} - \frac{x ^{2}}{16} = 1

x^{2} - y^{2} - 4 x - 2 y - 13 = 0

- 4 x^{2} + y^{2} - 2 y = 3

5 y^{2} - 2 x^{2} = 9

What is the asymptotes of 3x^2-15y^2+2x-3y=4 ?
The asymptotes of 3x^2-15y^2+2x-3y=4 is y=(3x+1)/(3sqrt(5))-1/10 ,\quad y=-(3x+1)/(3sqrt(5))-1/10