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chwala
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Homework Statement
[/B]The normal to a curve at a point P cuts the y-axis at T and N is the foot of the perpendiculor from P to the y axis. If for all P, T is always 1 unit below N, find the equation of the curve.
Homework Equations
The Attempt at a Solution
Point T has co ordinates ## (0,y)##
and point N has co ordinates ##(0,y+1)## Points T and N intersect at point P ,(a right angle ) having co ordinates##P (X,Y),## thus let the gradients be ##m## and ##-m## respectively, we then have ##(Y-y)/x=m## and ##(Y-(y+1))/x=-m## on solving we shall have ##(Y-y)=1/2## implying that ##(Y-y)/x=m##≡ ##1/2/x=m## , where ##m=1/2x## which is the gradient. we know that the gradient of a curve is always equal to the gradient of the tangent, to get the equation we need to ##∫dy/dx ## wrt x...
the answer to this problem is ##y=k-1/2x^2##
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