What is 3x^2-8y^2+12x+16y+20=0 ?

The solution to 3x^2-8y^2+12x+16y+20=0 is Hyperbola with (h,k)=(-2,1),a=sqrt(2),b= 4/(sqrt(3))

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3x^2-8y^2+12x+16y+20=0

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

(h, k) = (- 2, 1), a = 2, b = \frac{4}{3}

Solution steps

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

Rewrite

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, 1), a = 2, b = \frac{4}{3}

f (x) = - 3 x^{2} + 6 x - 1

\frac{( y + 2 ) ^{2}}{16} - \frac{( x - 3 ) ^{2}}{9} = 1

f (x) = x^{2} - 2 x - 8

x^{2} - y = 4

16 x^{2} + y^{2} = 16

What is 3x^2-8y^2+12x+16y+20=0 ?
The solution to 3x^2-8y^2+12x+16y+20=0 is Hyperbola with (h,k)=(-2,1),a=sqrt(2),b= 4/(sqrt(3))