Question

Pedal equation of requal to 2a divided by 1+cos theta

Answer 1

Answer:

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/2 or For polar subtangent, OT r tan φ = 2a/ (1 - cos θ) . tan(π - θ/2) Read 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