What is 3x^2-y^2+30x+8y=-71 ?

The solution to 3x^2-y^2+30x+8y=-71 is Hyperbola with (h,k)=(-5,4),a=2sqrt(3),b=2

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3x^2-y^2+30x+8y=-71

3 x^{2} - y^{2} + 30 x + 8 y = - 71

(h, k) = (- 5, 4), a = 23, b = 2

Solution steps

3 x^{2} - y^{2} + 30 x + 8 y = - 71

Rewrite

3 x^{2} - y^{2} + 30 x + 8 y = - 71

in the form of a standard hyperbola equation

\frac{( y - 4 ) ^{2}}{( 2 3 ) ^{2}} - \frac{( x - ( - 5 ) ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 5, 4), a = 23, b = 2

4 x^{2} - 4 y^{2} + 28 x - 8 y + 53 = 0

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{9} = 1

9 x^{2} - 4 y^{2} - 72 x + 16 y + 92 = 0

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

3 x^{2} - 3 y^{2} - 6 x = 0

What is 3x^2-y^2+30x+8y=-71 ?
The solution to 3x^2-y^2+30x+8y=-71 is Hyperbola with (h,k)=(-5,4),a=2sqrt(3),b=2