What is the foci ((y+7/2)^2)/(25)-((x-9/2)^2)/(25)=1 ?

The foci ((y+7/2)^2)/(25)-((x-9/2)^2)/(25)=1 is (9/2 ,(-7+10sqrt(2))/2),(9/2 ,(-7-10sqrt(2))/2)

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foci ((y+7/2)^2)/(25)-((x-9/2)^2)/(25)=1

foci

\frac{( y + \frac{7}{2} ) ^{2}}{25} - \frac{( x - \frac{9}{2} ) ^{2}}{25} = 1

(\frac{9}{2}, \frac{- 7 + 10 2}{2}), (\frac{9}{2}, \frac{- 7 - 10 2}{2})

Solution steps

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

Calculate Hyperbola properties

\frac{( y + \frac{7}{2} ) ^{2}}{25} - \frac{( x - \frac{9}{2} ) ^{2}}{25} = 1 :

Up-down Hyperbola with

(h, k) = (\frac{9}{2}, - \frac{7}{2}), a = 5, b = 5

(\frac{9}{2}, - \frac{7}{2} + c), (\frac{9}{2}, - \frac{7}{2} - c)

Compute

c :

c = 5^{2} + 5^{2} : 52

(\frac{9}{2}, - \frac{7}{2} + 52), (\frac{9}{2}, - \frac{7}{2} - 52)

Refine

(\frac{9}{2}, \frac{- 7 + 10 2}{2}), (\frac{9}{2}, \frac{- 7 - 10 2}{2})

y^{2} - 4 x^{2} = 16

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

x^{2} - \frac{y ^{2}}{25} = 1

x^{2} - 9 y^{2} = 144

\frac{( x - 1 ) ^{2}}{25} - \frac{( y + 3 ) ^{2}}{9} = 1

What is the foci ((y+7/2)^2)/(25)-((x-9/2)^2)/(25)=1 ?
The foci ((y+7/2)^2)/(25)-((x-9/2)^2)/(25)=1 is (9/2 ,(-7+10sqrt(2))/2),(9/2 ,(-7-10sqrt(2))/2)