Question

eliminate the parameter and write the corresponding rectangular equation... PLEASE! : x=4+ 2 cos theta and y=-1+2 sin theta

Answer 1

is it (x-4)^2/16+(y+1)^2/4=1 ?

Answer 2

and the graph please

Answer 3

x = 4 + 2cos(t)

x-4 = 2cos(t)

(x-4)^2 = (2cos(t))^2

(x-4)^2 = 4cos^2(t)

--------------------------

y = -1+2sin(t)

y+1 = 2sin(t)

(y+1)^2 = (2sin(t))^2

(y+1)^2 = 4sin^2(t)

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So we have

(x-4)^2 = 4cos^2(t)

and

(y+1)^2 = 4sin^2(t)


Add the equations to get


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

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

(x-4)^2 + (y+1)^2 = 4(1)

(x-4)^2 + (y+1)^2 = 4


So it's a circle center at (4,-1) with a radius of 2

Answer 4

I got that:) can u show a pic of the graph @jim_thompson5910

Answer 5

Use a graphing calculator to get

Answer 6

thats what i got:D

Answer 7

that's great

Answer 8

I have another one..do mind

Answer 9

no go ahead

Answer 10

Ok can you graph these ? the first problem is: evolute of ellipse: x= 2 cos^3 theta and y=4 sin^3 theta.

Answer 11

And the second problem is : serpentine curve: x=1/2 cot theta and y=4 sin theta cos theta

Answer 12

are u there @jim_thompson5910

Answer 13

yeah just graphing, one sec

Answer 14

kk

Answer 15

here's the first graph

Answer 16

ok great

Answer 17

second is serpentine curve: x=1/2 cot theta and y=4 sin theta cos theta

Answer 18

and here's the graph for that

Answer 19

thanks so much!!

Answer 20

you're welcome

Answer 21

hi Jim, how did you plus in cosine to the third into the graphing calculator. Is there some special key to raising cosine theta to the third