What is -4x^2+56x+y^2-188=0 ?

The solution to -4x^2+56x+y^2-188=0 is Hyperbola with (h,k)=(7,0),a=sqrt(2),b=2sqrt(2)

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-4x^2+56x+y^2-188=0

- 4 x^{2} + 56 x + y^{2} - 188 = 0

(h, k) = (7, 0), a = 2, b = 22

Solution steps

- 4 x^{2} + 56 x + y^{2} - 188 = 0

Rewrite

- 4 x^{2} + 56 x + y^{2} - 188 = 0

in the form of a standard hyperbola equation

\frac{( x - 7 ) ^{2}}{( 2 ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (7, 0), a = 2, b = 22

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

4 x^{2} - 9 y^{2} + 144 = 0

- 4 x^{2} + 5 y^{2} + 21 x - 5 y + 28 = 0

4 (x - 4)^{2} - 25 (y - 1)^{2} = 100

x^{2} - 2 y^{2} = 16

What is -4x^2+56x+y^2-188=0 ?
The solution to -4x^2+56x+y^2-188=0 is Hyperbola with (h,k)=(7,0),a=sqrt(2),b=2sqrt(2)