Identify the curve by finding the Cartesian Equation:
r = 4sec(theta)

so the formulas that can be used here are:
x = rcos(theta)
y = rsin(theta)
x^2 + y^2 = r^2
tan(theta) = y/x

I need to get it to be in the form x^2 + y^2 = r^2

I did:
r = 4sec(theta)
r = 4(r/x)
x = 4
but now... I'm stuck because no matter what I do with that x = 4, I'm don't end up with x^2 + y^2 = (number) format.

Any help would be appreciated. Ty.

Question

Identify the curve by finding the Cartesian Equation:
r = 4sec(theta)

so the formulas that can be used here are:
x = rcos(theta)
y = rsin(theta)
x^2 + y^2 = r^2 
tan(theta) = y/x

I need to get it to be in the form x^2 + y^2 = r^2

I did:
r = 4sec(theta)
r = 4(r/x)
x = 4
but now... I'm stuck because no matter what I do with that x = 4, I'm don't end up with x^2 + y^2 = (number) format. 

Any help would be appreciated. Ty.

anonymous · Answer

Example in book, number 21, page 663, section 10.3
just like this but reverse.
its y=2 convert to polar coordinates
r = 2csc(theta) is the answer from the solution manual. 

thus, x=4 is correct.