eliminate parameter in parametric equation

teffy3001

so the question is:

eliminate the parameter in the pair of parametric equations

x = h + a secθ
y = k + b tanθ

to find the corresponding rectangular equation.


im taking an online course of calculus and i cant find an explanation of how to do this anywhere...ive been trying but it just doesnt make sense to me yet....any help?

Dick

sec^2(x)-tan^2(x)=1. So solve for the sec and tan, square and subtract.

teffy3001

how do i solve for sec and tan?
sorry but this calculus thing...its been a while for me

Dick

Not a calc question. x=h+a*sec(t), x-h=a*sec(t), (x-h)/a=sec(t). That sort of thing. Remember?

teffy3001

thanks, so if i do all that...then that answers my first question too?

Dick

You will have eliminated theta, right? Isn't that the problem?

teffy3001

i dont even know...this is so confusing. sorry to bother you with this....

Dick

Just try doing it. Solve for sec and tan - then square both expressions and subtract.

teffy3001

so i would get ((x-h)/a)^2 - ((y-k)/b)^2 = 1 ?

Dick

Exactly. That wasn't so bad, was it?

teffy3001

haha no thanks.