Let denote a curve y=y(x) which is in the first quadrant and let the point (1,0) lie on it. Let the tangent to at a point P intersect the y-axis at Y_P. If PY_P has length 1 for each point P on , then which of the following options is/are correct?

JEE Advanced 2019 Mathematics question

Mathematics Application of Derivatives JEE Advanced 2019

Let denote a curve which is in the first quadrant and let the point lie on it. Let the tangent to at a point intersect the -axis at . If has length 1 for each point on , then which of the following options is/are correct?

(A)Correct
(B)Correct
(C)
(D)

Answer: (A),(B)

Solution

The tangent at meets the -axis at . . The curve lies in the first quadrant (, ) and passes through , so must increase as decreases from 1, i.e. :

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Question ID VK-026854