i am having one idea i.e first obtain locus of above coordinate system

x^2/3 +y^2/3=16 now obtain dy/dx for this curve that comes out to be -tan(t)

now obtain equation of tangent to this curve

but what i understand that you want to apply concept of gradient in above problem but that always gives equation of normal

limpfisch

2012-05-10 17:29:13

r(t) = ((4cost)^3, (4sint)^3) for -pi<=pi

i tried just finding T(t) by using r'(t)/|r'(t)| but i keep getting a giant mess which is no good given i have to find the normal vector and curvature later. Please help.