How do you find the rectangular equation for r=secthetar=secθ?

1 Answer
Epsilon
May 25, 2018

see below

Explanation:

The relation between rectangular and polar coordinates is
x=rcostheta ,y=rsin thetax=rcosθ,y=rsinθ ---(1)
Squaring and adding, we get r^2=x^2+y^2r2=x2+y2
From (1), we have y/x=tan thetayx=tanθ
the given equation is r=sec thetar=secθ
Squaring, we get r^2=sec^2 thetar2=sec2θ or r^2=1+tan^2 thetar2=1+tan2θ
The required rectangular equation is
x^2+y^2=1+y^2/x^2x2+y2=1+y2x2 or
x^4+x^2y^2-x^2-y^2=0x4+x2y2−x2−y2=0

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