Question

Question 11 Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Class X1 - Maths -Conic Sections Page 262

Answer 1

concept :- if foci lies on y-axis . I mean if co-ordinate of foci is like ( 0, ±c ) then, equation of hyperbola will be of the form
y²/a² - x²/b² = 1.also c² = a² + b² and,
length of conjugate axis = 2b.

A/C to question,
Foci ( 0, ± 13) = ( 0, ± c)
hence, c = 13---------------(1)
and length of conjugate axis = 24 = 2b
b = 12 ------------(2)

now, from above concept .
c² = a² + b²
put values of b and c from equations (1) and (2)
13² = a² + 12²
169 = a² + 144
169 - 144 = a²
a² = 25 ---------(3)

hence, equation of hyperbola by putting equations (2) and (3)
y²/25 - x²/144 = 1