Polar Form of Conic Sections - Part 2

In this video, we discuss the variations of the polar form of conic sections, which we derived in the previous video as r = ed/(1+ecosθ)
This equation can also be written as r = l/(1+ecosθ), where l denotes the length on the semi-latus rectum.
If we mirror the geometric definition of the conic, you will see that equally, we can have r = l/(1-ecosθ).
And if we rotate this geometry by 90˚ in the counter clockwise direction, we can have r = l/(1+esinθ) or r = l/(1-esinθ)
Thanks for watching. Please give me a "thumbs up" if you have found this video helpful.
Please ask me a maths question by commenting below and I will try to help you in future videos.
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[@stimulantdaimamld2099]

excellent

[@sarthakpapney3125]

sir how 'mirror image' give us the negative of cos(theta) in the denominator? please reply sir please.....

[@MasterWuMathematics]

Try this exercise. Refer to part 1 here kzbin.info/www/bejne/gZbJg2Z6htyqaqs, and try constructing the geometry the other way (i.e. create the mirror image) to derive the polar form. I think you'll find your answer.

[@laxmipapney7182]

thank you so much sir really you explain very beautifully I love your videos sir please keep doing good work.. love from India

[@anzatzi]

unclear why ed = l ?

[@MasterWuMathematics]

This may take me several videos to explain, which I will do in time. But it might be a long time...

[@astroblogger]

If you've seen the first video you saw that for the point P (r,θ) ; e = r/distance to the directrix. If you do the same formulation for P (r2,θ=90°), you will see that e = l/distance to the directrix. Now, from this relation you could eliminate d earily and get the desired result trivially.