Question

R=2sec(theta) converted into a cartesian equation

Answer 1

`\bf r=2sec(\theta )\qquad \begin{cases} x=rcos(\theta )\\ (x)/(r)=cos(\theta ) \end{cases}\qquad \implies r=2\cdot \cfrac{1}{cos(\theta )}\implies r=\cfrac{2}{~~(x)/(r)~~} \\\\\\ r=\cfrac{(2)/(1)}{~~(x)/(r)~~}\implies r=\cfrac{2r}{x}\implies x=\cfrac{2~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies x=2`