What is -x^2+2y^2+28y+14=0 ?

The solution to -x^2+2y^2+28y+14=0 is Hyperbola with (h,k)=(0,-7),a=sqrt(42),b=2sqrt(21)

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-x^2+2y^2+28y+14=0

- x^{2} + 2 y^{2} + 28 y + 14 = 0

(h, k) = (0, - 7), a = 42, b = 221

Solution steps

- x^{2} + 2 y^{2} + 28 y + 14 = 0

Rewrite

- x^{2} + 2 y^{2} + 28 y + 14 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 7 ) ) ^{2}}{( 42 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 2 21 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 7), a = 42, b = 221

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

9 y^{(2)} - x^{(2)} = 36

x - 3 = \frac{y ^{2} + 9}{x + 3}

x^{2} - 16 y^{2} - 16 = 0

4 x^{2} - 9 y^{2} = 15

What is -x^2+2y^2+28y+14=0 ?
The solution to -x^2+2y^2+28y+14=0 is Hyperbola with (h,k)=(0,-7),a=sqrt(42),b=2sqrt(21)