1 answer

The polar equation of the form #x^2+2y-1=0# is .........?

Question:

The polar equation of the form #x^2+2y-1=0# is .........?

Answers

#1/r=1+sintheta#

Explanation:

The relation between polar coordinates #(r,theta)# and rectangular coordinates #(x,y)# is given by #x=rcostheta# and #y=rsintheta#.

Hence #x^2+2y-1=0# can be written as

#r^2cos^2theta+2rsintheta-1=0#

or #r^2-r^2sin^2theta+2rsintheta-1=0#

or #r^2-(r^2sin^2theta-2rsintheta+1)=0#

or #r^2-(rsintheta-1)^2=0#

or #(r-rsintheta+1)(r+rsintheta-1)=0#

and either #r+rsintheta-1=0# i.e. #1/r=1+sintheta#

or #r-rsintheta+1=0# i.e. #1/r=sintheta-1#

In fact #1/r=1+sintheta# and #1/r=sintheta-1# both indicate same parabola (shown below).
graph{x^2+2y=1 [-5.167, 4.833, -3.36, 1.64]}

.

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