CAT 2017 Coordinate Geometry Question (Hard)

Question

The shortest distance of the point from the curve is

Accepted Answer

Step 1 We are given the curve y x - 1 x 1 First, express this piecewise. There are critical points at and . - For , So - For , So - For , So Thus, piecewise y -2x x leq -1 2 -1 leq x leq 1 2x x geq 1 We need the shortest distance from . Since , we consider . At , . But our point is . We can compute

CAT 2017

Quantitative

Coordinate Geometry

Hard

The shortest distance of the point $\left(\tfrac{1}{2}, 1\right)$ from the curve $y = |x - 1| + |x + 1|$ is

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