Question #124395

(a) Find radius of curvature of curve:

x2+ xy + y2= 4 at point (–2, 0)


1
Expert's answer
2020-06-29T19:14:32-0400

To find Radius of curvature


formula: R= (1+y(x))2/3y(x))\frac{(1+y'(x))^{2/3}}{\left | y''(x)) \right |}

Solution :


y'(x)= (2x+y)x+2y\frac{-(2x+y)}{x+2y}

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= (12)2/33\frac{(1-2)^{2/3}}{\left | 3 \right |} =-1/3


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