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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Expert Answer

Adnaan Franks
Answered 2020-12-15 Author has 92 answers

Step 1 The standard polar equation for lines is given by rcos(θθ)=r where (r,θ)is the foot of the | from the (0, 0) to the line and r0

Step 2 For example: If (4,45) is the foot of the perpendicular, then the polar equation of the line is rcos(θ45)=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+ecosθ

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+cosθ

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=ke1ecosθ

Step 6 For example: The polar equation for a conic with eccentricity (e=1)and directrix x=3 is r=3×111×cosθ r=31cosθ

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=ke1esinθ

Step 10 For example: The polar equation for a conic with eccentricity (e=0.5)and directrix y=4 is r=4×0.510.5sinθ r=210.5sinθ

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