What is the foci ((y-9/2)^2)/(49)-((x-7/2)^2)/(49)=1 ?

The foci ((y-9/2)^2)/(49)-((x-7/2)^2)/(49)=1 is (7/2 ,(9+14sqrt(2))/2),(7/2 ,(9-14sqrt(2))/2)

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foci ((y-9/2)^2)/(49)-((x-7/2)^2)/(49)=1

foci

\frac{( y - \frac{9}{2} ) ^{2}}{49} - \frac{( x - \frac{7}{2} ) ^{2}}{49} = 1

(\frac{7}{2}, \frac{9 + 14 2}{2}), (\frac{7}{2}, \frac{9 - 14 2}{2})

Solution steps

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

Calculate Hyperbola properties

\frac{( y - \frac{9}{2} ) ^{2}}{49} - \frac{( x - \frac{7}{2} ) ^{2}}{49} = 1 :

Up-down Hyperbola with

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

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

Compute

c :

c = 7^{2} + 7^{2} : 72

(\frac{7}{2}, \frac{9}{2} + 72), (\frac{7}{2}, \frac{9}{2} - 72)

Refine

(\frac{7}{2}, \frac{9 + 14 2}{2}), (\frac{7}{2}, \frac{9 - 14 2}{2})

9 x^{2} - 4 y^{2} + 18 x - 27 = 0

\frac{x ^{2}}{8} - \frac{y ^{2}}{8} = 1

\frac{y ^{2}}{64} - \frac{x ^{2}}{49} = 1

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

- 4 x^{2} + y^{2} = 36

What is the foci ((y-9/2)^2)/(49)-((x-7/2)^2)/(49)=1 ?
The foci ((y-9/2)^2)/(49)-((x-7/2)^2)/(49)=1 is (7/2 ,(9+14sqrt(2))/2),(7/2 ,(9-14sqrt(2))/2)