Question

Question 8 Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Class X1 - Maths -Conic Sections Page 262

Answer 1

concept : if ( 0, ± a) are vertices of hyperbola.
then equation of hyperbola will be of the form
y²/a² - x²/b² = 1 . and foci of hyperbola will be ( 0, ±c) where c² = a² + b²


A/C to question,
vertices ( 0, ± 5) = ( 0, ± a)
hence, a = 5 ------------------------(1)

foci ( 0, ± c) = ( 0, ± 8)
hence, c = 8 ----------------(2)

now, use c² = a² + b²
put the values of c and b from equations (1) and (2) . we get ,
8² = 5² + b²
64 = 25 + b²
64 - 25 = 39 = b² -------------(3)

now, equation of hyperbola by putting values of a² and b² using equations (2) and (3).
y²/25 - x²/39 = 1