What is the foci ((x-7)^2)/(100)-((y+8)^2)/(25)=1 ?

The foci ((x-7)^2)/(100)-((y+8)^2)/(25)=1 is (7+5sqrt(5),-8),(7-5sqrt(5),-8)

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foci ((x-7)^2)/(100)-((y+8)^2)/(25)=1

foci

\frac{( x - 7 ) ^{2}}{100} - \frac{( y + 8 ) ^{2}}{25} = 1

(7 + 55, - 8), (7 - 55, - 8)

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 7 ) ^{2}}{100} - \frac{( y + 8 ) ^{2}}{25} = 1 :

Right-left Hyperbola with

(h, k) = (7, - 8), a = 10, b = 5

(7 + c, - 8), (7 - c, - 8)

Compute

c :

c = 1 0^{2} + 5^{2} : 55

(7 + 55, - 8), (7 - 55, - 8)

\frac{x ^{2}}{4} - (\frac{y + 1}{16})^{2} = 1

\frac{x ^{2}}{36} - \frac{y ^{2}}{2} = 1

x^{2} - 4 y^{2} + 16 y - 32 = 0

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

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0

What is the foci ((x-7)^2)/(100)-((y+8)^2)/(25)=1 ?
The foci ((x-7)^2)/(100)-((y+8)^2)/(25)=1 is (7+5sqrt(5),-8),(7-5sqrt(5),-8)