Pedal Equation of a Polar Curve - Polar Curves - Engineering Mathematics - 2

TL;DR

The pedal equation of a polar curve is derived by expressing the polar curve in terms of the distance of the tangent from the pole and the radius vector.

Transcript

hello in this session we'll discuss about pedal equation of a polar curve so so far we have seen in polar curve let's say the polar curve is given as r equal to f of theta for which we have found the perpendicular distance of the tangent to the pole given by the expression of p equal to r sine phi now r as f of theta and p which we have already fou... Read More

Key Insights

• 😑 The pedal equation of a polar curve is derived by expressing the curve in terms of the distance of the tangent from the pole and the radius vector.
• 😡 The angle between the radius vector and tangent is given by tan phi = r(d theta / d r).
• ❓ Eliminating theta from the equations results in the pedal equation.
• 🐬 In some cases where phi cannot be found explicitly, manipulating the equation p = r sin phi can lead to the pedal equation.
• 👻 The pedal equation allows for a different representation of the polar curve.
• 🦻 Understanding the pedal equation can aid in solving problems related to polar curves.
• 🐻‍❄️ The pedal equation can be useful in various applications, such as analyzing the movement of objects in polar coordinates.

Questions & Answers

Q: What is the pedal equation of a polar curve?

The pedal equation of a polar curve is obtained by expressing the curve in terms of the distance of the tangent from the pole and the radius vector.

Q: How is the angle between the radius vector and tangent determined?

The angle between the radius vector and tangent is given by tan phi = r(d theta / d r), where r is the radius and theta is the angle.

Q: How can theta be eliminated from the equations to obtain the pedal equation?

By substituting the value of cot phi as 1 / (r * d r / d theta) in the equation, theta can be eliminated and the pedal equation can be derived.

Q: What is an alternative method to derive the pedal equation?

In cases where it is not possible to find phi explicitly, the equation p = r sin phi can be manipulated to obtain an equation in terms of p and r, which is the pedal equation.

Summary & Key Takeaways

• The pedal equation of a polar curve is derived by expressing the polar curve in terms of the distance of the tangent from the pole and the radius vector.

• The angle between the radius vector and tangent is given by tan phi = r(d theta / d r).

• By eliminating theta from the equations, an equation in terms of p and r can be obtained, known as the pedal equation.