A hyperbola with its centre at the origin and transverse axis along the -axis…

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A hyperbola with its centre at the origin and transverse axis along the

x

-axis satisfies the following conditions: • The constant difference of the focal distances of any point on it is

14

units. • Its eccentricity is

\dfrac{5}{3}

. (i) Determine the exact numerical values of

a,\,b

and

c

. (ii) Write the standard equation of the hyperbola. (iii) Find the equations of its asymptotes and the coordinates of its foci.