What is 4x^2-3y^2+8x+16=0 ?

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

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4x^2-3y^2+8x+16=0

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

(h, k) = (- 1, 0), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{2 ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = 2, b = 3

(x + 5)^{2} - (y + 6)^{2} = 20

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

\frac{x ^{2}}{100} - \frac{y ^{2}}{75} = 1

64 x^{2} - 36 y^{2} + 192 x + 36 y - 441 = 0

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

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