What is 3y^2-12x^2-36y-48x+48=0 ?

The solution to 3y^2-12x^2-36y-48x+48=0 is Hyperbola with (h,k)=(-2,6),a=2,b=1

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3y^2-12x^2-36y-48x+48=0

3 y^{2} - 12 x^{2} - 36 y - 48 x + 48 = 0

(h, k) = (- 2, 6), a = 2, b = 1

Solution steps

3 y^{2} - 12 x^{2} - 36 y - 48 x + 48 = 0

Rewrite

3 y^{2} - 12 x^{2} - 36 y - 48 x + 48 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, 6), a = 2, b = 1

\frac{( y + 7 ) ^{2}}{4} - \frac{( x + 2 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 2 ) ^{2}}{9} = 1

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

x^{2} - 4 y^{2} + 6 x + 24 y - 40 = 0

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{16} = 1

What is 3y^2-12x^2-36y-48x+48=0 ?
The solution to 3y^2-12x^2-36y-48x+48=0 is Hyperbola with (h,k)=(-2,6),a=2,b=1