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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Compute

c :

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

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

Refine

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

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{169} = 1

y^{2} - 49 x^{2} - 14 y - 490 x - 1125 = 0

\frac{x ^{2}}{25} - \frac{y ^{2}}{4} = 1

4 y^{2} - x^{2} + 6 x + 8 y + 4 = 0

- 9 x^{2} + y^{2} + 6 y - 27 = 0

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