What is the asymptotes of 4x^2-y^2+16x+6y=9 ?

The asymptotes of 4x^2-y^2+16x+6y=9 is y=2(x+2)+3,\quad y=-2(x+2)+3

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asymptotes of 4x^2-y^2+16x+6y=9

asymptotes

4 x^{2} - y^{2} + 16 x + 6 y = 9

y = 2 (x + 2) + 3, y = - 2 (x + 2) + 3

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} + 16 x + 6 y = 9 :

Right-left Hyperbola with

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

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

Refine

y = 2 (x + 2) + 3, y = - 2 (x + 2) + 3

9 x^{2} - 25 y^{2} - 72 x + 369 = 0

6 x^{2} - \frac{2}{3} y^{2} = 4

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

\frac{x ^{2}}{4} - \frac{y ^{2}}{16} = 1

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

What is the asymptotes of 4x^2-y^2+16x+6y=9 ?
The asymptotes of 4x^2-y^2+16x+6y=9 is y=2(x+2)+3,\quad y=-2(x+2)+3