What is 4x^2-9y^2+8x+72y-203=0 ?

The solution to 4x^2-9y^2+8x+72y-203=0 is Hyperbola with (h,k)=(-1,4),a=(3sqrt(7))/2 ,b=sqrt(7)

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4x^2-9y^2+8x+72y-203=0

4 x^{2} - 9 y^{2} + 8 x + 72 y - 203 = 0

(h, k) = (- 1, 4), a = \frac{3 7}{2}, b = 7

Solution steps

4 x^{2} - 9 y^{2} + 8 x + 72 y - 203 = 0

Rewrite

4 x^{2} - 9 y^{2} + 8 x + 72 y - 203 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{3 7}{2} ) ^{2}} - \frac{( y - 4 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 4), a = \frac{3 7}{2}, b = 7

\frac{27 x ^{2}}{4} - 9 y^{2} - 54 x - 18 y + \frac{225}{4} = 0

9 y^{2} - 16 x^{2} - 90 y - 128 x - 175 = 0

x^{2} - 1 y^{2} = 88

\frac{x ^{2}}{64} - \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{8} = 1

What is 4x^2-9y^2+8x+72y-203=0 ?
The solution to 4x^2-9y^2+8x+72y-203=0 is Hyperbola with (h,k)=(-1,4),a=(3sqrt(7))/2 ,b=sqrt(7)