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1-the normal to a curve at p (x,y) meets the x-axis at G if the dist of G from origin is twice the abscissa of p , find curve 2- u see in this q - dy/dx( e to the power x + 1/e to the power x)+1=0 find soln as real ans is c1e to the power x + c2 e to the power -x why diff ans 3-1-the normal to a curve at p (x,y) meets the x-axis at G if the dist of G from origin is twice the abscissa of p , find curve respected sir plz check the soln again which u provid 1- find the eqn of curve which is such that the portion of the axis of x cut off b/w the origin and tangent at any pt is proportional to the ordinate of that pt

1-the normal to a curve at p (x,y) meets the x-axis at G if the dist of G from origin is twice the abscissa of p , find curve

2- u see in this q - dy/dx( e to the power x + 1/e to the power x)+1=0 find soln as real ans is c1e to the power x + c2 e to the power -x why diff ans
3-1-the normal to a curve at p (x,y) meets the x-axis at G if the dist of G from origin is twice the abscissa of p , find curve
respected sir plz check the soln again which u provid

1- find the eqn of curve which is such that the portion of the axis of x cut off b/w the origin and tangent at any pt is proportional to the ordinate of that pt

Grade:12

1 Answers

mamillapelly bhagath
33 Points
8 years ago
P(x, y) and G(2x, 0) are 2 points on the normal. So, slope of the normal is, m=0-y2x-x=-yx This means that the slope of the curve to which the normal was drawn is = -1m=xy Thus, the equation of the curve is:- Y-y=xy(X-x)i.e., Yy-y2=Xx-x2i.e., Xx-Yy=x2-y2 (2) xy=1yx ?xyyx=1?log (xyyx)=log 1?log(xy)+log(yx)=0 ?ylogx + xlogy=0?ddx(ylogx + xlogy)=ddx(0)?yx+logxdydx+logy+xydydx=0 ?dydx(logx+xy)=-logy-yx?dydx=-logy+yx(logx+xy) ?dydx=-(xlogy+y)y(ylogx+x)x?dydx=-y2+xy logyx2+xy logx

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