What is the asymptotes of 4x^2-y^2-24x-6y+23=0 ?

The asymptotes of 4x^2-y^2-24x-6y+23=0 is y=2(x-3)-3,\quad y=-2(x-3)-3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

asymptotes of 4x^2-y^2-24x-6y+23=0

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

y^{2} - 4 x^{2} = 16

What is the asymptotes of 4x^2-y^2-24x-6y+23=0 ?
The asymptotes of 4x^2-y^2-24x-6y+23=0 is y=2(x-3)-3,\quad y=-2(x-3)-3