What is 2x^2-4y^2+12x+8y+10=0 ?

The solution to 2x^2-4y^2+12x+8y+10=0 is Hyperbola with (h,k)=(-3,1),a=sqrt(2),b=1

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2x^2-4y^2+12x+8y+10=0

2 x^{2} - 4 y^{2} + 12 x + 8 y + 10 = 0

(h, k) = (- 3, 1), a = 2, b = 1

Solution steps

2 x^{2} - 4 y^{2} + 12 x + 8 y + 10 = 0

Rewrite

2 x^{2} - 4 y^{2} + 12 x + 8 y + 10 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 1), a = 2, b = 1

\frac{x ^{2}}{11} - \frac{y ^{2}}{16} = 1

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

5 x^{2} - 3 y^{2} = 8

d^{2} = (3 - 10 t)^{2} + (2 - 40 t)^{2}

- \frac{1}{2} (\frac{x ^{2}}{2} - 100 x) + 3 y^{2} - 150 y = 100

What is 2x^2-4y^2+12x+8y+10=0 ?
The solution to 2x^2-4y^2+12x+8y+10=0 is Hyperbola with (h,k)=(-3,1),a=sqrt(2),b=1