Answer to Question #281785 in Differential Geometry | Topology for chaitu

Question #281785

find the radius of the curvature at (acostheta^3,asintheta^3) on the curve x^2/3+y^2/3=a^2/3


1
Expert's answer
2021-12-22T13:11:02-0500

radius of the curvature:

"R=\\frac{(1+(dy\/dx)^2)^{3\/2}}{|d^2y\/dx^2|}"


"2x\/3+2yy'\/3=0"

"y'=-\\frac{x}{y}"


"y''=-\\frac{y-xy'}{y^2}"


at point "(acos \\theta^3 ,asin \\theta ^3):"

"y'=-cot\\theta^3"


"y''=-\\frac{sin\\theta^3-cos^2\\theta^3\/sin\\theta^3}{sin^2\\theta ^3}"


"R=\\frac{sin^2\\theta ^3(1+cot^2\\theta^3)^{3\/2}}{sin\\theta^3-cos^2\\theta^3\/sin\\theta^3}"


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