Question

the radius of curvature of x^2+y^2=4 is​

Answer 1

Answer:

Radius = 2 units

Note:

★ The general equation of a circle is given by ;

(x-h)² + (y-k)² = r² , where (h,k) is the centre and r is the radius of yours circle .

Solution ;

Here ,

The given equation of curvature is ;

x² + y² = 4 .

Clearly ,

This the equation of a circle which can be rewritten as ;

(x - 0)² + (y - 0)² = 2²

On comparing with the general equation of the circle (x-h)² + (y-k)² = r²

We have ;

h = 0

k = 0

r = 2

Clearly ,

Center of the curvature is (0,0) , ie ; origin and the radius of the curvature is 2 units .

Hence ,

Radius of curvature = 2 units .