How do you convert # r = 4 csc (theta) cot (theta)# to rectangular form?

1 Answer
P dilip_k
May 7, 2016

#y^2 =4x#

Explanation:

If the rectangular coordinate of a point be #(x,y)# and its corresponding polar coordinate be #(r,theta)# then we know that #x = rcostheta and y = rsintheta#

Our given equation in polar form is
# r = 4 csc (theta) cot (theta)=4/sintheta*costheta/sintheta#
#=>rsin^2theta =costheta#

Multiplying both sides by r
#=>r^2sin^2theta =4rcostheta#
#=>(rsintheta)^2 =4rcostheta#

Putting # rcostheta=x and rsintheta=y# we have the equation in rectangular form

#=>y^2 =4x#

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