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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: wildareal on August 05, 2010, 12:40:44 am

Title: Polar to Cartesian
Post by: wildareal on August 05, 2010, 12:40:44 am: r=a/(1+Cos(x))
Title: Re: Polar to Cartesian
Post by: /0 on August 05, 2010, 01:33:53 am: $r = \frac{a}{1+\cos{\theta}}$ .

$\Rightarrow r = \frac{a}{1+\frac{x}{r}}$ (Using $x = r\cos{\theta}$ )

$\Rightarrow a = r+x$

$a -x= \sqrt{x^2+y^2}$ (Using $r = \sqrt{x^2+y^2}$ )

$a^2-2ax+x^2 = x^2+y^2$

$a^2-2ax=y^2$

$x = \frac{1}{2a}(a^2-y^2)$