Hyperbola - 1

1. Find the following properties of hyperbola for the given equation

(i) Points where hyperbola intersects the x-axis
(ii) eccentricity
(iii) foci
(iv) distance between the foci
(v) length of the latus rectum

Equation of the hyperbola is x2. Equation of hyperbola in its standard form

x²/16 - y²/9² = 1

Concepts to be used

For the hyperbola x²/a² - y²/b² = 1


The hyperbola intersects x axis at (a,0) and (-a,0).


b² = a²(e²-1)
Where e = eccentricity

Focus is (ae,0)


Solution:
Hyperbola given is x²/16 - y²/9 = 1

a =4, b= 3

Intersecting points on the x axis = (4,0) and (-4,0)
Eccentricity 9 = 16(e²-1)
=> 9/16 + 1 = e²
=> 25/16 = e²
=> e = 5/4

foci are (±ae,) = (5,0) and (-5,0)

distance between the foci = 10

Length of the latus rectum = 2b²/a = 18/4 = 9/2