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Question

At what point the slope of the tangent to the curve x2 + y2 − 2x − 3 = 0 is zero

(a) (3, 0), (−1, 0)
(b) (3, 0), (1, 2)
(c) (−1, 0), (1, 2)
(d) (1, 2), (1, −2)

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Solution

(d) (1, 2), (1, −2)

Let (x1, y1) be the required point.

Since, the point lie on the curve.Hence, x12+y12-2x1-3=0 ...1Now, x2+y2-2x-3=0 2x+2y dydx-2=0dydx=2-2x2y=1-xyNow,Slope of the tangent = dydxx1, y1= 1-x1y1Slope of the tangent=0 (Given)1-x1y1=01-x1=0x1=1From (1), we getx12+y12-2x1-3=01+y12-2-3=0y12-4=0y1=±2So, the points are 1, 2 and 1, -2.

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