(a) Find radius of curvature of curve:
x2+ xy + y2= 4 at point (–2, 0)
To find Radius of curvature
formula: R=
Solution :
y'(x)=
At (-2,0), y'(x)= -(-4+0)/(-2)=-2
Y"(x)= [(x+2y)(-2-y')+(2x+y)(1+2y')]/(x+2y)2= (3xy'-3y)/(x+2y)2
At (-2,0), y''(x)= -6)(-2)/4 = 3
Hence substituting in formula , R= =-1/3
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