 # What are the standard equations for lines and conic sections in polar coordinates? Give examples. Amari Flowers 2020-12-14 Answered
What are the standard equations for lines and conic sections in polar coordinates? Give examples.
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Step 1 The standard polar equation for lines is given by $rcos\left(\theta -{\theta }_{\circ }\right)={r}_{\circ }$ where

Step 2 For example: If $\left(4,{45}^{\circ }\right)$ is the foot of the perpendicular, then the polar equation of the line is $r\mathrm{cos}\left(\theta -{45}^{\circ }\right)=4$

Step 3 The standard polar equation for a conic with eccentricity (e) and directrix $x=k$ and focus at the (0, 0) is given by $r=\frac{ke}{1+e\mathrm{cos}\theta }$

Step 4 For example: The polar equation for a conic with eccentricity is $r=\frac{5×1}{1+1×cos\theta }$ $r=\frac{5×1}{1+\mathrm{cos}\theta }$

Step 5 The standard polar equation for a conic with eccentricity (e) and directrix $x=-k$ and focus at the (0, 0) is given by $r=\frac{ke}{1-ecos\theta }$

Step 6 For example: The polar equation for a conic with eccentricity is $r=\frac{3×1}{1-1×cos\theta }$ $r=\frac{3}{1-cos\theta }$

Step 7 The standard polar equation for a conic with eccentricity (e) and directrix $y=k$ and focus at the (0, 0) is given by $r=\frac{ke}{1+esin\theta }$

Step 8 For example: The polar equation for a conic with eccentricity is $r=\frac{2×0.5}{1+0.5sin\theta }$ $r=\frac{1}{1+0.5sin\theta }$

Step 9 The standard polar equation for a conic with eccentricity (e) and directrix $y=-k$ and focus at the (0, 0) is given by $r=\frac{ke}{1-esin\theta }$

Step 10 For example: The polar equation for a conic with eccentricity is $r=\frac{4×0.5}{1-0.5sin\theta }$ $r=\frac{2}{1-0.5sin\theta }$