What is the foci (x^2)/(a^2)-(y^2)/(b^2)=1 ?

The foci (x^2)/(a^2)-(y^2)/(b^2)=1 is (sqrt(a^2+b^2),0),(-sqrt(a^2+b^2),0)

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foci (x^2)/(a^2)-(y^2)/(b^2)=1

foci

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

(a^{2} + b^{2}, 0), (- a^{2} + b^{2}, 0)

Solution steps

(h + c, k), (h - c, k)

Calculate Hyperbola properties

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = a, b = b

(0 + c, 0), (0 - c, 0)

Compute

c :

c = a^{2} + b^{2}

(0 + a^{2} + b^{2}, 0), (0 - a^{2} + b^{2}, 0)

Refine

(a^{2} + b^{2}, 0), (- a^{2} + b^{2}, 0)

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

\frac{( y + 6 ) ^{2}}{36} - \frac{( x + 4 ) ^{2}}{48} = 1

9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0

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

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

What is the foci (x^2)/(a^2)-(y^2)/(b^2)=1 ?
The foci (x^2)/(a^2)-(y^2)/(b^2)=1 is (sqrt(a^2+b^2),0),(-sqrt(a^2+b^2),0)