How do you convert #r=4sec(theta)(1+ tan(theta))# into cartesian form?

Question

2261 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-26T09:53:48

#1/4=1/x+1/y#

Polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# are related as

#x=rcostheta# and #y=rsintheta#, i.e. #tantheta=y/x#

Hence, #r=4sectheta(1+tantheta)# can be written as

#rcostheta=4(1+tantheta)#

or #y=4(1+y/x)#

or #xy=4x+4y#

or #(xy)/(4xy)=(4x)/(4xy)+(4y)/(4xy)#

or #1/4=1/y+1/x# or #1/4=1/x+1/y#