Mathematics

Problem

A hyperbola is centred at the origin with its transverse axis along the

x

-axis. The distance between its foci is

10\text{ units}

and the constant difference of the focal distances of any point on the curve is

8\text{ units}

. a. (i) Determine the lengths of the semi-transverse axis

a

and the semi-focal distance

c

. b. (ii) Calculate the value of

b

and write the standard equation of the hyperbola.