A tangent to the curve y = f(x) at P(x, y) cuts the x-axis and the y-axis at A and B, respectively, such that BP : AP = 3 : 1. If f(1) = 1 then

JEE Advanced Mathematics question

A tangent to the curve at cuts the -axis and the -axis at and , respectively, such that . If then

Answer: (A),(B)

The tangent at is . Its intercepts are

A = (x - y,\ 0), B = (0,\ y - x).

lies on segment with , so . The -coordinates give

y = 14(y - x)

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Question ID VK-110618