Question

Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation

9x^2 - (y^2)/16 =1
by -2 unit(s) right and 4 unit(s) up

x=?
y=?

Answer 1

you know that sec^2(t)-tan^2(t) = 1

so, let

x = sec(t)/3
y = 4tan(t)

Answer 2

oops. That gives the untranslated parameterization. You want to shift things, so

x = sec(t)/3 - 2
y = 4tan(t) + 4

so that

9(x+2)^2 - (y-4)^2/16 = 1