What is 7x^2-9y^2-14x+72y-200=0 ?

The solution to 7x^2-9y^2-14x+72y-200=0 is Hyperbola with (h,k)=(1,4),a=3,b=sqrt(7)

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7x^2-9y^2-14x+72y-200=0

7 x^{2} - 9 y^{2} - 14 x + 72 y - 200 = 0

(h, k) = (1, 4), a = 3, b = 7

Solution steps

7 x^{2} - 9 y^{2} - 14 x + 72 y - 200 = 0

Rewrite

7 x^{2} - 9 y^{2} - 14 x + 72 y - 200 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 4), a = 3, b = 7

(y + 1)^{2} = x^{2} - x

x, x^{2} + 6 x + 34 = h (x)^{2}

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0

x^{2} = (13 y^{2} + 1)

What is 7x^2-9y^2-14x+72y-200=0 ?
The solution to 7x^2-9y^2-14x+72y-200=0 is Hyperbola with (h,k)=(1,4),a=3,b=sqrt(7)