Question

Eliminate the parameter. x = 4 cos t, y = 4 sin t

Answer 1

Sin^2 + cos^2 = 1
so,
   (x/4)^2 + (y/4)^2 = 1

we got rid of t.

Answer 2

Answer:

$x^2+y^2=16$

Step-by-step explanation:

Given: $x=4\cos t, y=4\sin t$

We need to eliminate the parameter t from parametric equation.

$x=4\cos t$

Square both sides

$x^2=(4\cos t)^2$

$x^2=16\cos^2 t$

$y=4\sin t$

Square both sides

$y^2=(4\sin t)^2$

$y^2=16\sin^2 t$

Add both equation

$x^2+y^2=16\cos^2t+16\sin^2t$

$x^2+y^2=16(\cos^2t+\sin^2t)$         $\because \sin^2\theta+\cos^2\theta = 1$

$x^2+y^2=16$

Hence, The new equation without parameter t would be $x^2+y^2=16$