Question

Question 3 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9y^2 – 4x^2 = 36

Class X1 - Maths -Conic Sections Page 262

Answer 1

9y² - 4x² = 36
dividing both sides by 36 .
9y²/36 - 4x²/36 = 36/36
y²/{36/9} - x²/{36/4} = 1
y²/ 4 - x²/ 9 = 1
y² /2² - x²/3² = 1 -------------------(1)


concept : if equation of hyperbola is in the form of y²/a² - x²/b² = 1.-------------(2)
then,
vertices ( 0, ± a)
foci ( 0, ± c) , where, c² = a² + b²
eccentricity ( e ) = c/a
Latusrectum = 2b²/a

now, compare equations (1) and (2),
a = 2 , and b = 3
then, c² = a² + b² = 2² + 3² = 4 + 9 = 13
c = √13.

now, vertices ( 0, ± a) = ( 0, ± 2)
foci ( 0, ± c) = ( 0, ± √13)
eccentricity ( e ) = c/a = √13/2
latusrectum = 2b²/a = 2×9/2 = 9