Question

เลี่ร์"1.16 9

Answer 1

The given equation of the hyperbola is x 2 16 − y 2 9 =1

x 2 16 − y 2 9 =1 .(1)

Since the transverse axis is along the x axis, equation of the hyperbola can be represented as x 2 a 2 − y 2 b 2 =1 .(2)

Comparing equations (1) and (2), we get

a=4 and b=3

Also, c 2 = a 2 + b 2 c 2 = 4 2 + 3 2 c 2 =16+9 c=5

Since x axis is the transverse axis, coordinates of Foci = (±c,0)=(±5,0)

Since x axis is the transverse axis, coordinates of Vertices = (±a,0)=(±4,0)

Eccentricity = e = c a = 5 4

Length of Latus rectum = 2 b 2 a = 2 (3) 2 4 = 9 2

Thus, the coordinates of foci of hyperbola x 2 16 − y 2 9 =1 are ( ±5,0 ) , coordinates of vertices are ( ±4,0 ) , eccentricity is 5 4 and length of latus rectum is 9 2 .