What is 4x^2-y^2+16x+6y=9 ?

The solution to 4x^2-y^2+16x+6y=9 is Hyperbola with (h,k)=(-2,3),a=2,b=4

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4x^2-y^2+16x+6y=9

4 x^{2} - y^{2} + 16 x + 6 y = 9

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

Solution steps

4 x^{2} - y^{2} + 16 x + 6 y = 9

Rewrite

4 x^{2} - y^{2} + 16 x + 6 y = 9

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{289} - \frac{( y - 70 ) ^{2}}{1600} = 1

16 x^{2} - 9 y^{2} - 64 x - 54 y - 161 = 0

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

y^{2} = x^{2} + 529

x^{2} + 79 = y^{2} + 18 x - 2 y

What is 4x^2-y^2+16x+6y=9 ?
The solution to 4x^2-y^2+16x+6y=9 is Hyperbola with (h,k)=(-2,3),a=2,b=4