Radius of Curvature

[14sohngenk]

Let T be the tangent line at the point P(x,y) to the graph of the curve x^(2/3)+y^(2/3)=a^(2/3), a>0. Show that the radius of curvature at P is three times the distance from the origin to the tangent line T.

HELP ME PLEASE !

 

[DrPhil]

Let T be the tangent line at the point P(x,y) to the graph of the curve x^(2/3)+y^(2/3)=a^(2/3), a>0. Show that the radius of curvature at P is three times the distance from the origin to the tangent line T.

HELP ME PLEASE !

\(\displaystyle \displaystyle x^{2/3} + y^{2/3} = a^{2/3}\)

Point \(\displaystyle P(x,y)\) is any point on the curve, and line T is tangent at that point. What is the slope of T? What is the 2nd derivative at P? How is the radius of curvature related to the 2nd derivative?

Let us see your work - else we don't know where you are getting stuck.

 

[HallsofIvy]

Do you know what "radius of curvature" is? Does your text have any formulas for "radius of curvature"?