find rectangular equation for each curve : x=2+4cost,y= 4sint -1?

Answer 1

(x-2)^2 + (y+1)^2
= (4 cos t)^2 + (4 sin t)^2
= 16 cos^2 t + 16 sin^2 t
= 16,

so you can describe the curve by the equation

(x-2)^2 + (y+1)^2 = 16,

which is the equation of a circle of radius 4 centered at the point (2,-1).

Answer 2

x=2+4cost, y= 4sint -1
so
x-2=4cost, and y+1=4sint
so
(x-2)^2=16cos^2 t and (y+1)^2=16sin^2 t
so
(x-2)^2+(y+1)^2=16cos^2 t + 16sin^2 t
(x-2)^2+(y+1)^2=16 since cos^2 t + sin^2 t =1

Answer 3

x=sqrt(t) y=3-t x^2=t and t=3-y subsequently : x^2 = 3-y y = 3- x^2 This graph is an the different way up quadratic with optimum element (0,3). y intercept (0,3) x intercepts (sqrt(3),0) and (-sqrt(3),0)