What is 4y^2-2x^2-4y-8x-15=0 ?

The solution to 4y^2-2x^2-4y-8x-15=0 is Hyperbola with (h,k)=(-2, 1/2),a=sqrt(2),b=2

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4y^2-2x^2-4y-8x-15=0

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

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

Solution steps

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

Rewrite

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

\frac{( x - 10 ) ^{2}}{36} - \frac{( y - 9 ) ^{2}}{36} = 1

y^{2} - 3 x^{2} - y + 16 x = 9

\frac{x ^{2}}{9} - \frac{y ^{2}}{36} = 1

- 9 x^{2} + 4 y^{2} - 36 = 0

What is 4y^2-2x^2-4y-8x-15=0 ?
The solution to 4y^2-2x^2-4y-8x-15=0 is Hyperbola with (h,k)=(-2, 1/2),a=sqrt(2),b=2