Question

Question 10 Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Class X1 - Maths -Conic Sections Page 262

Answer 1

concept : if Foci lies on X-axis e.g (±c , 0), then equation of hyperbola will be of the form,
x²/a² - y²/b² = 1. and c² = a² + b²,
also length of transverse axis = 2a.

A/C to question,
Foci ( ±5 , 0) = ( ± c , 0)
hence, c = 5 ----------------------(1)

and Length of transverse axis = 8 = 2a
a = 4 ------------------(2)

from above concept ,
c² = a² + b² , put the values of c and a from equations (1) and (2).
5² = 4² + b²
25 = 16 + b²
b² = 9---------------------------(3)

hence, equation of hyperbola from equations (2) and (3) .
x²/4² - y²/9 = 1 or, x²/16 - y²/9 = 1.