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Problem

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19 Nov 2021

Given information

The given equation of polar curve is .

The angle between the radial line and the tangent line is constant.

The equation of the polar curve with the property that the angle between the radial line and the tangent line is a constant must be of the form , where and are constants.

Step-by-step explanation

Step 1.
  • From the exercise 69, it can be noticed that where is the angle between the tangent line at any point and the radial line at that point to the curve .
  • The angle between the radial line and the horizontal line is constant. Therefore the tangent of the angle is also constant that implies the value of  is constant.
  • Rewrite the equation .
  • The equation is a differential equation.

   

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