The Curve Described By (x2+y2)2=x2 Constains Exact

CSRoger2

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The curve described by (x2+y2)2=x2 constains exactly 4 points where the tangent line is horizontal. Find them.

 

Answer No.1

Anonymous

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X2+y2= x taking derivative 2yy'+2x=1 as y'= (1-2x)/2y tangent line is horizontal means slope = 0 equating u will get x = 1/2 or -1/2 when x = 1/2 y =√(1/2-1/4) = 1/2 when x = -1/2 y = √(1/2-1/4) = 1/2 so 4 points are (1/2 , 1/2),(1/2 , -1/2),(-1/2 , 1/2),(-1/2 , -1/2)

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