Example 3.  Consider the parabola  [Graphics:Images/CurvatureMod_gr_34.gif] and the point  (1,f(1)) = (1,1)  on the curve.  
Find the radius of curvature and the circle of curvature.

Solution 3.

[Graphics:../Images/CurvatureMod_gr_35.gif]



[Graphics:../Images/CurvatureMod_gr_36.gif]
[Graphics:../Images/CurvatureMod_gr_37.gif]
[Graphics:../Images/CurvatureMod_gr_38.gif]

[Graphics:../Images/CurvatureMod_gr_39.gif]
[Graphics:../Images/CurvatureMod_gr_40.gif]
[Graphics:../Images/CurvatureMod_gr_41.gif]

[Graphics:../Images/CurvatureMod_gr_42.gif]
[Graphics:../Images/CurvatureMod_gr_43.gif]
[Graphics:../Images/CurvatureMod_gr_44.gif]



[Graphics:../Images/CurvatureMod_gr_45.gif]


[Graphics:../Images/CurvatureMod_gr_46.gif]

[Graphics:../Images/CurvatureMod_gr_47.gif]
[Graphics:../Images/CurvatureMod_gr_48.gif]
[Graphics:../Images/CurvatureMod_gr_49.gif]
[Graphics:../Images/CurvatureMod_gr_50.gif]
[Graphics:../Images/CurvatureMod_gr_51.gif]
[Graphics:../Images/CurvatureMod_gr_52.gif]



[Graphics:../Images/CurvatureMod_gr_53.gif]


[Graphics:../Images/CurvatureMod_gr_54.gif]

[Graphics:../Images/CurvatureMod_gr_55.gif]
[Graphics:../Images/CurvatureMod_gr_56.gif]
[Graphics:../Images/CurvatureMod_gr_57.gif]
[Graphics:../Images/CurvatureMod_gr_58.gif]
[Graphics:../Images/CurvatureMod_gr_59.gif]
[Graphics:../Images/CurvatureMod_gr_60.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004