at what point is the tangent to the curve x+y^2=1 parallel to the line x+2y=0

Question

arka mitra · Answer

when the tangent to the curve x+y 2 =1 is parallel to another curve , then that means the derivative of this equation is equal to the derivative of the other curve i.e. x+2y =0 therefore, the derivative of the first curve is 1+ (2y)dy/dx=0 simplifying it we get dy/dx=-1/2y--------------(i) now derivative of the other curve is 1+ 2dy/dx=0 simplifying it we get dy/dx=-1/2---------------(ii) now if we compare these two equation we would see that we get y=1 [from -1/2y=-1/2] at the point when y is equal to 1 x is equal to 0 . This we can get from the equation of the curve ...... so, the point where the curve x+y 2 =1 is parallel to the curve x+2y=0 is (0,1) hope this helps....;)

Chetan Mandayam Nayakar · Answer

x+y^2=1, upon implicit differentiation we get 1=-2yy',y'=-1/2y=slope of line=-(1/2),thus -1/2=-1/2y,y=+1,x=1-y^2=1-1=0 therefore the point is (0,1)

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at what point is the tangent to the curve x+y^2=1 parallel to the line x+2y=0

at what point is the tangent to the curve x+y^2=1 parallel to the line x+2y=0

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