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Find the equation of hyperbola whose ver...

Find the equation of hyperbola whose vertices are `(0,pm5)` and focii are `(0,pm10)`

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The vertices and foci of hyperbola are on y-axis. Therefore, is conjugate hyperbola.
Here b = 5 and be = 10
`rArr" "e=2`
`:." "a^(2)=b^(2)(e^(2)-1)`
`=25(4-1)=75`
`:.` Equation of hyperbola
`(y^(2))/(b^(2))-(x^(2))/(a^(2))=1`
`rArr" "(y^(2))/(25)-(x^(2))/(75)=1`
`rArr" "3y^(2)-x^(2)=75`.
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