What is 4x^2-y^2-16x+2y+11=0 ?

The solution to 4x^2-y^2-16x+2y+11=0 is Hyperbola with (h,k)=(2,1),a=1,b=2

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4x^2-y^2-16x+2y+11=0

4 x^{2} - y^{2} - 16 x + 2 y + 11 = 0

(h, k) = (2, 1), a = 1, b = 2

Solution steps

4 x^{2} - y^{2} - 16 x + 2 y + 11 = 0

Rewrite

4 x^{2} - y^{2} - 16 x + 2 y + 11 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = 1, b = 2

(\frac{( y + 4 )}{9})^{2} - (\frac{( x - 3 )}{25})^{2} = 1

\frac{( x - 3 ) ^{2}}{25} - \frac{( y - 1 ) ^{2}}{4} = 1

\frac{x ^{2}}{7} - \frac{y ^{2}}{6} = 1

25 x^{2} - y^{2} + 50 x + 6 y - 9 = 0

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

What is 4x^2-y^2-16x+2y+11=0 ?
The solution to 4x^2-y^2-16x+2y+11=0 is Hyperbola with (h,k)=(2,1),a=1,b=2