What is 4x^2-y^2+16x+8y=36 ?

The solution to 4x^2-y^2+16x+8y=36 is Hyperbola with (h,k)=(-2,4),a=3,b=6

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4x^2-y^2+16x+8y=36

4 x^{2} - y^{2} + 16 x + 8 y = 36

(h, k) = (- 2, 4), a = 3, b = 6

Solution steps

4 x^{2} - y^{2} + 16 x + 8 y = 36

Rewrite

4 x^{2} - y^{2} + 16 x + 8 y = 36

in the form of a standard hyperbola equation

\frac{( x - ( - 2 ) ) ^{2}}{3 ^{2}} - \frac{( y - 4 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 4), a = 3, b = 6

X^{2} - 3 Y^{2} + 2 X + 6 Y - 1 = 0

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

16 y^{2} - 9 x^{2} + 36 x + 96 y - 36 = 0

4 x^{2} - 25 y^{2} - 8 x - 100 y - 196 = 0

- \frac{x ^{2}}{25} + \frac{y ^{2}}{144} = 1

What is 4x^2-y^2+16x+8y=36 ?
The solution to 4x^2-y^2+16x+8y=36 is Hyperbola with (h,k)=(-2,4),a=3,b=6