Question

One among the following is the correct explanation of pedal equation of an polar curve, r=f (θ), p=r sin(∅) (where p is the length of the perpendicular from the pole to the tangent & ∅ is the angle made by tangent to the curve with vector drawn to curve from pole)is _______

(a) It is expressed in terms of p & θ only

(b) It is expressed in terms of p & ∅ only

(c) It is expressed in terms of r & θ only

(d) It is expressed in terms of p& r only

The question was asked in final exam.

My question is based upon Polar Curves in portion Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (d) It is expressed in terms of p& r only

The explanation is: It is expressed in terms of p& r only

where p=r sin(∅) & \(tan⁡∅ = \frac{r}{\frac{dr}{dθ}} = r (\frac{dr}{dθ})\)

& r=f (θ) or after solving we get direct relationship between p & r as

\(\frac{1}{p^2} = \frac{1}{r^2} cosec^2∅.\)