Let y=y(x) be a curve passing through the point (1,1) and satisfying dydx+√(x2−1)(y2−1)xy=0. If the curve passes through the point (√2,k), then the largest value of |[k]| is (Here, [.] represents the greatest integer function)

Let y=y(x) be a curve passing through the point (1,1) and satisfying d

1.	Let y=y(x) be a curve passing through the point (1,1) and satisfying dydx+√(x2−1)(y2−1)xy=0. If the curve passes through the point (√2,k), then the largest value of \|[k]\| is (Here, [.] represents the greatest integer function)
Answer» Let $y = y (x)$ be a curve passing through the point $(1, 1)$ and satisfying $\frac{d y}{d x} + \frac{\sqrt{(x^{2} - 1) (y^{2} - 1)}}{x y} = 0.$ If the curve passes through the point $(\sqrt{2}, k),$ then the largest value of $\| [k] \|$ is (Here, $[.]$ represents the greatest integer function)