What is 4x^2-9y^2-16x+18y-7=0 ?

The solution to 4x^2-9y^2-16x+18y-7=0 is Hyperbola with (h,k)=(2,1),a=sqrt(7/2),b=(sqrt(14))/3

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4x^2-9y^2-16x+18y-7=0

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

Solution steps

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

Rewrite

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{( \frac{7}{2} ) ^{2}} - \frac{( y - 1 ) ^{2}}{( \frac{14}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

10 x^{2} - 4 y^{2} - 8 x - 10 y - 12 = 0

y^{2} - 4 x^{2} = 16

x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

\frac{( x ^{(2)} )}{( 16 ) + ( y - 4 ) ^{(2)}} = 1

- 9 x^{2} + 25 y^{2} - 100 y - 125 = 0

What is 4x^2-9y^2-16x+18y-7=0 ?
The solution to 4x^2-9y^2-16x+18y-7=0 is Hyperbola with (h,k)=(2,1),a=sqrt(7/2),b=(sqrt(14))/3