What is 96+32x+16x^2-16y^2=0 ?

The solution to 96+32x+16x^2-16y^2=0 is Hyperbola with (h,k)=(-1,0),a=sqrt(5),b=sqrt(5)

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96+32x+16x^2-16y^2=0

96 + 32 x + 16 x^{2} - 16 y^{2} = 0

(h, k) = (- 1, 0), a = 5, b = 5

Solution steps

96 + 32 x + 16 x^{2} - 16 y^{2} = 0

Rewrite

96 + 32 x + 16 x^{2} - 16 y^{2} = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = 5, b = 5

- 4 x^{2} + y^{2} - 16 x - 52 = 0

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

\frac{x ^{2}}{49} - \frac{y ^{2}}{81} = 1

x^{2} - 2 y^{2} - 2 x - 12 y = 35

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

What is 96+32x+16x^2-16y^2=0 ?
The solution to 96+32x+16x^2-16y^2=0 is Hyperbola with (h,k)=(-1,0),a=sqrt(5),b=sqrt(5)