What is 137+6y=y^2-24x-x^2 ?

The solution to 137+6y=y^2-24x-x^2 is Hyperbola with (h,k)=(-12,3),a=sqrt(2),b=sqrt(2)

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137+6y=y^2-24x-x^2

137 + 6 y = y^{2} - 24 x - x^{2}

(h, k) = (- 12, 3), a = 2, b = 2

Solution steps

137 + 6 y = y^{2} - 24 x - x^{2}

Rewrite

137 + 6 y = y^{2} - 24 x - x^{2}

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( 2 ) ^{2}} - \frac{( x - ( - 12 ) ) ^{2}}{( 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 12, 3), a = 2, b = 2

\frac{y ^{2}}{25} - \frac{( x - 5 ) ^{2}}{16} = 1

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

9 x^{2} - 72 x - 4 y^{2} - 40 y + 44 = 36

4 x^{2} + 24 x - 2 y^{2} + 36 = 36

\frac{( y - 3 ) ^{2}}{4} - \frac{( x + 1 ) ^{2}}{16} = 1

What is 137+6y=y^2-24x-x^2 ?
The solution to 137+6y=y^2-24x-x^2 is Hyperbola with (h,k)=(-12,3),a=sqrt(2),b=sqrt(2)