What are the standard equations for lines and conic sections in polar coordinates? Give examples.

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Adnaan Franks · Accepted Answer

Step 1 The standard polar equation for lines is given by rcos(θ−θ∘)=r∘ where (r∘,θ∘)is the foot of the | from the (0, 0) to the line and r∘≥0  Step 2 For example: If (4,45∘) is the foot of the perpendicular, then the polar equation of the line is rcos⁡(θ−45∘)=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=ke1+ecos⁡θ   Step 4 For example: The polar equation for a conic with eccentricity (e=1)and directrix x=5 is r=5×11+1×cosθ r=5×11+cos⁡θ   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=ke1−ecosθ   Step 6 For example: The polar equation for a conic with eccentricity (e=1)and directrix x=−3 is r=3×11−1×cosθ r=31−cosθ   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=ke1+esinθ   Step 8 For example: The polar equation for a conic with eccentricity (e=0.5)and directrix y=2 is r=2×0.51+0.5sinθ r=11+0.5sinθ   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=ke1−esinθ   Step 10 For example: The polar equation for a conic with eccentricity (e=0.5)and directrix y=−4 is r=4×0.51−0.5sinθ r=21−0.5sinθ

What are the standard equations for lines and conic sections in polar coordinates? Give examples.

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