Eliminate parameter and write corresponding rectangular equation.
x=sec theta , y=tan theta
- i dont know where to start
2007-06-21 21:25:28 · 4 answers · asked by fcb10121 1 in Science & Mathematics ➔ Mathematics
theta is the parameter.
To eliminate it, square and subtract the two given equations.
So, x^2 - y^2 = sec^2 theta - tan^2 theta = 1.
Thus, the equation x^2 - y^2 = 1 is free from parameter theta.
2007-06-21 21:30:51 · answer #1 · answered by Madhukar 7 · 1⤊ 0⤋
Use the Pythagorean identity tan^2(x)+1=sec^2(x).
y^2+1=x^2
2007-06-21 21:33:55 · answer #2 · answered by Anonymous · 1⤊ 0⤋
You have the parametric equations.
x = secθ
y = tanθ
x² - y² = sec²θ - tan²θ = 1
x² - y² = 1
This is the equation of a pair of hyperbolas centered on the origin.
2007-06-21 22:54:18 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
1 + tan^2(x) = sec^2(x).
Therefore:
1 + y^2 = x^2
y^2 = x^2 - 1.
2007-06-21 21:33:43 · answer #4 · answered by Anonymous · 1⤊ 0⤋