Q9 of 71 Page 27

Write the equation of the hyperbola whose vertices are (±3, 0) and foci at (±5, 0).

Given: Vertices are (±3, 0) and foci are (±5, 0)


To find: equation of the hyperbola


Formula used:


Standard form of the equation of hyperbola is,



Vertices of hyperbola are given by (±a, 0)


Foci of hyperbola are given by (±ae, 0)


Vertices are (±3, 0) and foci are (±5, 0)


Therefore,


a = 3 and ae = 5


⇒ 3 × e = 5



b2 = a2(e2 – 1)







⇒ b2 = 16


Equation of hyperbola:




Hence, required equation of hyperbola is


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