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Question

Write the coordinates of the point on the curve y2 = x where the tangent line makes an angle π4 with x-axis.

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Solution

Let the required point be (x1, y1).
The tangent makes an angle of 45o with the x-axis.
∴ Slope of the tangent = tan 45o = 1

Since, the point lies on the curve.Hence, y12=x1Now, y2=x2ydydx=1dydx=12ySlope of the tangent = dydxx1, y1=12y1Given:12y1=12y1=1y1=12Now,x1=y12=122=14x1, y1=14, 12

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