Question

6. 49y2 - 16r2784

Answer 1

The given equation of the hyperbola is 49 y 2 −16 x 2 =784 .

49 y 2 −16 x 2 =784 (1)

The above equation can be written as,

y 2 784 49 − x 2 784 16 =1 y 2 16 − x 2 49 =1

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

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

a=4 and b=7

c 2 = a 2 + b 2 c 2 = 4 2 + 7 2 c 2 =16+49 c 2 =65 c= 65

Since y axis is the transverse axis, coordinates of Foci = (0,±c)=(0,± 65 )

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

Eccentricity = e = c a = 65 4

Length of Latus rectum = 2 b 2 a = 2 (7) 2 4 = 49 2

Thus, the coordinates of foci of hyperbola 49 y 2 −16 x 2 =784 are ( 0,± 65 ) ,coordinates of vertices are ( 0,±4 ) , eccentricity is 65 4 and length of latus rectum is 49 2 .