Parametrics Help (1 Viewer)

[OH1995]

Hello wonderful people,

Would you please be able to help me with this question:

Eliminate the parameter and hence find the cartesian equation of the curve;

x=1+2tanø and y=3secø-4

Thanks!

 

[RivalryofTroll]

(x-1)/2 = tanx
(y+4)/3 = secx

Since sec^2x - tan^2x = 1

Yeah, you know what to do now.

 

[Aesytic]

y = 3sec(theta) - 4
y+4 = 3sec(theta)
sec^2(theta) = (y+4)^2/9 ----- 1

x=1+2tan(theta)
tan(theta) = (x-1)/2
tan^2(theta) = (x-1)^2/4 ----- 2

1 - 2:
sec^2(theta) - tan^2(theta) = (y+4)^2/9 - (x-1)^2/4
1 = (y+4)^2/9 - (x-1)^2/4

 

[OH1995]

Oh wow, thanks. Haha I didn't see the trig identity!