Question

Question 9 Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Class X1 - Maths -Conic Sections Page 262

Answer 1

concept : if
$\frac{ {y}^{2} }{ {a}^{2} } - \frac{ {x}^{2} }{ {b}^{2} } = 1$
is the equation of hyperbola then,
foci = ( 0, ± c) where c² = a² + b²
vertices = ( 0, ± a)


Here, vertices ( 0, ± 3) = ( 0, ± a) .
hence, a = 3 --------------(1)

foci ( 0, ± c ) = ( 0, ± 5)
hence, c = 5
so, c² = a² + b² [ from concept ]
5² = 3² + b²
25 - 9 = b² => b² = 16 -------------(2)

now, equation of hyperbola is
y²/9 - x²/16 = 1