Question
Find the equation of a hyperbola whose vertices lie on y-axis, centre is at the origin, the distance between the foci is 16 and eccentricity is
Solution
The vertices of the hyperbola lie on the y-axis.
∴ The equation of the hyperbola in standard form is ...(i)
The foci are
The distance between them is 2c = 16 (given) c = 8
Eccentricity, e =
∴ c = 8 ae = 8
or
Now,
Hence, from (i), the equation of the hyperbola is: or