Eliminate the parameter in the pair of parametric equations to find the corresponding rectangular question.

x=h+ asecQ
y=k+ tanQ

secθ = (x-h)/a

tanθ = (y-k)

since sec^2 θ = 1+tan^2 θ

(x-h)^2/a^2 = 1+(y-k)^2
or,
(x-h)^2/a^2 - (y-k)^2 = 1

which is a horizontal hyperbola centered at (h,k).