What is 9x^2-4y^2+90x+189=0 ?

The solution to 9x^2-4y^2+90x+189=0 is Hyperbola with (h,k)=(-5,0),a=2,b=3

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9x^2-4y^2+90x+189=0

9 x^{2} - 4 y^{2} + 90 x + 189 = 0

(h, k) = (- 5, 0), a = 2, b = 3

Solution steps

9 x^{2} - 4 y^{2} + 90 x + 189 = 0

Rewrite

9 x^{2} - 4 y^{2} + 90 x + 189 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 5 ) ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 5, 0), a = 2, b = 3

3 x^{2} - y^{2} + 7 x - y + 18 = 0

- x^{2} + 4 x + 3 y^{2} - 18 y + 8 = 0

7 x^{2} - 9 y^{2} = 63

x^{2} - y^{2} - x + y - (- 10) = 0

y^{2} = (\frac{6}{5})^{2} + (2 - x)^{2}

What is 9x^2-4y^2+90x+189=0 ?
The solution to 9x^2-4y^2+90x+189=0 is Hyperbola with (h,k)=(-5,0),a=2,b=3