Mathematics

Mathematics

Problem

The slope of normal at any point (x,y)(x, y), x>0x > 0, y>0y > 0 on the curve y=y(x)y = y(x) is given by x2xy−x2y2−1\frac{x^2}{xy - x^2y^2 - 1}. If the curve passes through the point (1,1)(1, 1), then e⋅y(e)e \cdot y(e) is equal to: [JEE MAINS - ONLINE - 2022] (1) 1−tan⁡(1)1+tan⁡(1)\frac{1 - \tan(1)}{1 + \tan(1)} (2) tan⁡(1)\tan(1) (3) 1 (4) 1+tan⁡(1)1−tan⁡(1)\frac{1 + \tan(1)}{1 - \tan(1)}

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