What is 16y^2-9x^2-112y+36x+124=0 ?

The solution to 16y^2-9x^2-112y+36x+124=0 is Hyperbola with (h,k)=(2, 7/2),a= 3/2 ,b=2

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16y^2-9x^2-112y+36x+124=0

16 y^{2} - 9 x^{2} - 112 y + 36 x + 124 = 0

(h, k) = (2, \frac{7}{2}), a = \frac{3}{2}, b = 2

Solution steps

16 y^{2} - 9 x^{2} - 112 y + 36 x + 124 = 0

Rewrite

16 y^{2} - 9 x^{2} - 112 y + 36 x + 124 = 0

in the form of a standard hyperbola equation

\frac{( y - \frac{7}{2} ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( x - 2 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, \frac{7}{2}), a = \frac{3}{2}, b = 2

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

\frac{( x - 6 ) ^{2}}{25} - (y + 1)^{2} = 1

\frac{( y - 6 ) ^{2}}{9} - (x - 6)^{2} = 1

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

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

What is 16y^2-9x^2-112y+36x+124=0 ?
The solution to 16y^2-9x^2-112y+36x+124=0 is Hyperbola with (h,k)=(2, 7/2),a= 3/2 ,b=2