Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.
x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π
A. x2 - y2 = 6; -6 ≤ x ≤ 6
B. x2 - y2 = 36; -6 ≤ x ≤ 6
C. x2 + y2 = 6; -6 ≤ x ≤ 6
D. x2 + y2 = 36; -6 ≤ x ≤ 6
D ?
4 answers
Yes it's D.
Thank you
Can someone show the work, please?
use trig identity- cos^2 t + sin^2 t = 1
x = 6 cos t, y = 6 sin t
square both: x^2 = 6cos^2 t y^2 = 6sin^2 t
combine: x^2 + y^2 = 6cos^2 t + 6sin^2
use trig identity to eliminate sin^2 t and cos^2 t
x^2 + y^2 = 1x6x6
x^2 + y^2 = 36
x = 6 cos t, y = 6 sin t
square both: x^2 = 6cos^2 t y^2 = 6sin^2 t
combine: x^2 + y^2 = 6cos^2 t + 6sin^2
use trig identity to eliminate sin^2 t and cos^2 t
x^2 + y^2 = 1x6x6
x^2 + y^2 = 36
1 answer