What is the asymptotes of x^2-4y^2-4x+24y-36=0 ?

The asymptotes of x^2-4y^2-4x+24y-36=0 is y= 1/2 (x-2)+3,\quad y=-1/2 (x-2)+3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

asymptotes of x^2-4y^2-4x+24y-36=0

asymptotes

x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0

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

Solution steps

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

Calculate Hyperbola properties

x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0 :

Right-left Hyperbola with

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

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{36} = 1

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

4 y^{2} - 5 x^{2} - 48 y - 10 x + 59 = 0

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

16 x^{2} - 25 y^{2} = 400

What is the asymptotes of x^2-4y^2-4x+24y-36=0 ?
The asymptotes of x^2-4y^2-4x+24y-36=0 is y= 1/2 (x-2)+3,\quad y=-1/2 (x-2)+3