Question

4. 16x2- 9y2 576

Answer 1

The given equation of the hyperbola is 16 x 2 −9 y 2 =576 .

16 x 2 −9 y 2 =576 (1)

The above equation can be written as,

x 2 576 16 − y 2 576 9 =1 x 2 36 − y 2 64 =1 x 2 6 2 − y 2 8 2 =1

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

On comparing equations (1) and (2), we get

a=6 and b=8

c 2 = a 2 + b 2 c 2 = 6 2 + 8 2 c 2 =36+64 c 2 =100 c=10

Since x axis is the transverse axis, coordinates of Foci = (±c,0)=(±10,0)

Since x axis is the transverse axis, coordinates of Vertices = (±a,0)=(±6,0)

Eccentricity = e = c a = 10 6 = 5 3

Length of Latus rectum = 2 b 2 a = 2 (8) 2 6 = 64 3

Thus, the coordinates of foci of hyperbola 16 x 2 −9 x 2 =576 are ( ±10,0 ) , coordinates of vertices are ( ±6,0 ) , eccentricity is 5 3 and length of latus rectum is 64 3 .