What is 3y^2-x^2+18y-4x+20=0 ?

The solution to 3y^2-x^2+18y-4x+20=0 is Hyperbola with (h,k)=(-2,-3),a=1,b=sqrt(3)

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3y^2-x^2+18y-4x+20=0

3 y^{2} - x^{2} + 18 y - 4 x + 20 = 0

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

Solution steps

3 y^{2} - x^{2} + 18 y - 4 x + 20 = 0

Rewrite

3 y^{2} - x^{2} + 18 y - 4 x + 20 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

9 y^{2} - x^{2} = 81

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

x^{2} - y^{2} + 4 x + 16 y - 69 = 0

- \frac{36 ( x - 3 ) ^{2}}{1} + \frac{25 ( y - 4 ) ^{2}}{1} = 900

x^{2} - 5 y^{2} = 3

What is 3y^2-x^2+18y-4x+20=0 ?
The solution to 3y^2-x^2+18y-4x+20=0 is Hyperbola with (h,k)=(-2,-3),a=1,b=sqrt(3)