Question

Question 12 Find the equation of the hyperbola satisfying the give conditions: Foci (± 3.5^0.5, 0), the latus rectum is of length 8.

Class X1 - Maths -Conic Sections Page 262

Answer 1

concept :- if foci (±c, 0) then, standard equation of hyperbola is x²/a² - y²/b² = 1 where c² = a²+ b² and length of latusrectum = 2b²/a .

here, Foci ( ±3√5, 0) = ( ±c, 0)
then, c = 3√5 and
length of latusrectum = 8 = 2b²/a
8 = 2b²/a
b² = 4a ------------------(1)

now, use from above concept ,
c² = a² + b²
(3√5)² = a² + b²
a² + b² = 45 ------------(2)

from equation (1) and (2)

a² + 4a = 45
a² + 4a - 45 = 0
a² + 9a - 5a - 45 = 0
a(a + 9) - 5(a + 9) = 0
(a - 5)(a + 9) = 0
a = 5 , - 9 but a ≠ -9 because a is distance .
hence, a = 5
b² = 4a = 4 × 5 = 20

hence, equation of hyperbola is
x²/5² - y²/20 = 1 or, x²/25 - y²/20 = 1