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Question

Find the coordinates of the point on the curve x+y=4 at which tangent is equally inclined to the axes.

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Solution

We havex+y=4x12+y12=412.1x12+12.1Y12.dydx=0dydx=12.x122.y12=yx
Since, tangent is equally inclined to the axes.
dydx=±1yx=±1yx=1y=xFrom Eq.(i).,y+y=42y=44y=16y=4 and x=4
So, the required coordinates are (4, 4).


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