Question

Find the pedal equation of r=2a/1+cos theta​ ​

Answer 1

Given 2a/ r = (1 - cosθ) Taking log on both sides, log2a = log r + log(1 – cosθ) On differentiation,  0 = 1/r . dr/dθ + sinθ/ 1 − cosθ or    1/r dr/dθ = - cotθ/2  dθ/dr = - (tan θ/2)/ r  Therefore    tan φ = rdθ/dr = r( -(tan θ/2)/ r) = - tanθ/2 =  tan ( π - θ/2) implying  φ = π − θ/2 Again, we know that, p = r sin φ = r sin (π - θ/2) = 2a/ (1 - cos θ) . sin θ/2  = 2a/ (2sin2) θ/2 . sin θ/2 implying p = a cosecθ/2Read more on Sarthaks.com - https://www.sarthaks.com/494358/prove-that-in-the-parabola-2a-r-1-cos-i-2-ii-p-a-cosec-2

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Answer 2

Answer:

Step-by-step explanation: