Question

determine the curvature of the circle x2+y2=25

Answer 1

The curvature of the circle x² + y² = 25 is 0.2

Given: The equation of the circle;

                x² + y² = 25

To Find: The curvature of the circle

Solution:

• The curvature of a circle is the measure of the curved surface of the circle and it is constant in all places.

• The curvature of a circle depends on the radius of the circle. It is equal to the reciprocal of the radius of the circle.

• The formula for determining the curvature of a circle is given by,

               R = 1 / r                                                             ...(1)

Where R = The curvature of a circle, r = radius of the circle.

Coming to the numerical, we are given;

The equation of the circle;

                x² + y² = 25

            ⇒ x² + y² = ( 5 )²

So, the radius of the circle (r) is = 5 units

The curvature of the circle can be calculated by putting the value of the radius of the circle in (1),

                 R = 1 / r  

             ⇒ R = 1 / 5

                     = 0.2

Hence, the curvature of the circle x² + y² = 25 is 0.2

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