What is y^2-3x^2-4x-1=0 ?

The solution to y^2-3x^2-4x-1=0 is Hyperbola with (h,k)=(-2/3 ,0),a= 1/3 ,b=sqrt(1/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^2-3x^2-4x-1=0

y^{2} - 3 x^{2} - 4 x - 1 = 0

(h, k) = (- \frac{2}{3}, 0), a = \frac{1}{3}, b = \frac{1}{3}

Solution steps

y^{2} - 3 x^{2} - 4 x - 1 = 0

Rewrite

y^{2} - 3 x^{2} - 4 x - 1 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{2}{3} ) ) ^{2}}{( \frac{1}{3} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{2}{3}, 0), a = \frac{1}{3}, b = \frac{1}{3}

\frac{( x - 1 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1

\frac{x ^{2}}{8} - \frac{y ^{2}}{6} = 1

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0

(x - 2)^{2} - (y - 4)^{2} = 81

What is y^2-3x^2-4x-1=0 ?
The solution to y^2-3x^2-4x-1=0 is Hyperbola with (h,k)=(-2/3 ,0),a= 1/3 ,b=sqrt(1/3)