What is 3x^2-y^2+18x+8y+38=0 ?

The solution to 3x^2-y^2+18x+8y+38=0 is Hyperbola with (h,k)=(-3,4),a=3sqrt(3),b=3

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3x^2-y^2+18x+8y+38=0

3 x^{2} - y^{2} + 18 x + 8 y + 38 = 0

(h, k) = (- 3, 4), a = 33, b = 3

Solution steps

3 x^{2} - y^{2} + 18 x + 8 y + 38 = 0

Rewrite

3 x^{2} - y^{2} + 18 x + 8 y + 38 = 0

in the form of a standard hyperbola equation

\frac{( y - 4 ) ^{2}}{( 3 3 ) ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 4), a = 33, b = 3

0 = 1 + y^{2} - x^{2}

y^{2} = x^{2} + 12 x + 32

- \frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{7} = 1

(x - 2 \cdot y) \cdot (x + 2 \cdot y) = 90005

x^{2} - y^{2} = 303

What is 3x^2-y^2+18x+8y+38=0 ?
The solution to 3x^2-y^2+18x+8y+38=0 is Hyperbola with (h,k)=(-3,4),a=3sqrt(3),b=3