Question

Foci Ct 5, 0), the transverse axis is of length810.Foci (± 5,0), th

Answer 1

The given coordinates of foci are ( ±5,0 ) .and length of transverse axis is 8.

Since the foci are on the x axis, the equation of the hyperbola is represented as,

x 2 a 2 − y 2 b 2 =1 , where x is the transverse axis.(1)

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

∴c=5

Length of transverse axis = 2a

So, 2a=8 a=4

a 2 + b 2 = c 2 4 2 + b 2 = 5 2 b 2 =25−16 b 2 =9 b=±3

Substitute the values of a and b in equation (1)

x 2 16 − y 2 9 =1

Thus, the equation of hyperbola with foci ( ±5,0 ) length of transverse axis 8 is x 2 16 − y 2 9 =1 .