What is 4x^2-9y^2-16x+36y+16=0 ?

The solution to 4x^2-9y^2-16x+36y+16=0 is Hyperbola with (h,k)=(2,2),a=2,b=3

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4x^2-9y^2-16x+36y+16=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{64} - \frac{y ^{2}}{81} = 1

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

a^{2} + 150 = b^{2} + 9

3 x^{2} - 5 y^{2} = 7

What is 4x^2-9y^2-16x+36y+16=0 ?
The solution to 4x^2-9y^2-16x+36y+16=0 is Hyperbola with (h,k)=(2,2),a=2,b=3