What is 4x^2-9y^2+16x+18y-11=0 ?

The solution to 4x^2-9y^2+16x+18y-11=0 is Hyperbola with (h,k)=(-2,1),a= 3/(sqrt(2)),b=sqrt(2)

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4x^2-9y^2+16x+18y-11=0

4 x^{2} - 9 y^{2} + 16 x + 18 y - 11 = 0

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

Solution steps

4 x^{2} - 9 y^{2} + 16 x + 18 y - 11 = 0

Rewrite

4 x^{2} - 9 y^{2} + 16 x + 18 y - 11 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(16) x^{2} + (256) x - (361) y^{2} - 3610 y + (4273) = 0

x, x^{2} + 10 x + 25 = x + k (x)^{2}

x^{2} - y^{2} = 280

x - y = - 3 x^{2} + 2 y^{2}

\frac{y - 3}{x - 3} - \frac{2 x + 1}{y + 1} = 0

What is 4x^2-9y^2+16x+18y-11=0 ?
The solution to 4x^2-9y^2+16x+18y-11=0 is Hyperbola with (h,k)=(-2,1),a= 3/(sqrt(2)),b=sqrt(2)