Question

Find the equation of osculating circles

Answer 1

y=1/2 x^2 at the point (1,1/2)

Answer 2

\[y=\frac{ 1 }{ 2 }x^2\]

Answer 3

@ganeshie8 can u help

Answer 4

never heard of it before sorry :( @AccessDenied

Answer 5

also never heard of this, although i'll give it a look on-line
>> http://en.wikipedia.org/wiki/Osculating_circle

Answer 6

ahh looks u need to find radius and center of curvature at given point

Answer 7

i dont remember doing these before, u doing vector calc right ?

Answer 8

yes, Calc 3

Answer 9

radius k=\[\frac{ 1 }{ (1+x^2)^{3/2}} at (1,.5) =2\sqrt{2}\]

Answer 10

no idea how to find center

Answer 11

According to http://en.wikipedia.org/wiki/Center_of_curvature
the center is "at a distance from the curve equal to the radius of curvature, lying on the normal vector"

Answer 12

drawing is helpful T= tangent, N= normal