Question

Write the equation using rectangular coordinates.

Answer 1

\[r=\frac{ 4 }{ 1-\cos(\Theta)}\]

Answer 2

@mathmate @johnweldon1993 @zepdrix @Luigi0210

Answer 3

I tried to cross multiply but i got stuck

Answer 4

use
x=r cos(theta); y=r sin(theta); r^2=x^2+y^2;
Cross multiply and substitute
r(1-cos(t)=4
r=4+cos(t)
substitute and simplify.

Answer 5

so
\[x ^{2}+y ^{2}=4+\cos (\Theta)\]

Answer 6

So minus 4 on both sides

Answer 7

OHH wait wait how about multiplying R on both sides

Answer 8

Wait, watch out: r^2=x^2+y^2
So you put a square-root sign on the left, or you square both sides!

Answer 9

Don't forget: r cos(theta)=x

Answer 10

So
x^2+y^2=4r+x?

Answer 11

and correction
r=4+cos(t)
should read
r=4+rcos(t), so that makes life simpler.

Answer 12

Wait why. i thought we have to multiply r on both sides to do that

Answer 13

My bad from the start:
use x=r cos(theta), y=r sin(theta), (x^2+y^2)=r^2
Then
r=4/(1-cos(theta))
cross multiply
r(1-cos(theta))=4
r - r cos(theta)=4
r=4+r cos(theta)
Now do the substitutions,
sqrt(x^2+y^2)=(4+x)
I would be tempted to square both sides and simplify.

Answer 14

Hmm i got that so after we get the x^2+y^2=4+x

I mean i factored and got the x+2 part

Answer 15

@mathmate

Answer 16

If you square both sides, you'd get
sqrt(x^2+y^2)=(4+x)
(x^2+y^2)=(4+x)^2
x^2+y^2=x^2+8x+16
cancel x^2 on each side
y^2=8x+16
Or if you want to write it as a parabola (with horizontal axis)
x=(1/8)y^2-2

Answer 17

Wow i over think things sometimes D: Thanks @mathmate