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The curve passing through the point (1,1...

The curve passing through the point `(1,1)` satisfies the differential equation `(dy)/(dx)+(sqrt((x^2-1)(y^2-1)))/(x y)=0` . If the curve passes through the point `(sqrt(2),k),` then the value of `[k]` is (where [.] represents greatest integer function)_____

Answer

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Knowledge Check

  • The gradient (slope) of a curve at any point (x, y) is (x^(2)-4)/(x^(2)) . If the curve passes through the point (2,7), then the equation of the curve is

    A
    `y=x+(4)/(x) +3`
    B
    `y=x+(4)/(x)+4`
    C
    `y=x^(2)+3x+4`
    D
    `y=x^(2)-3x+6`

  • The gradient (siope) of a curve at any point (x,y) is (x^(2)-4)/(x^(2)) . If the curve passes through the point (2 , 7) , then the equation of the curve is ,

    A
    `y = x + (4)/(x) + 3 `
    B
    `y = x + (4)/(x) + 4 `
    C
    `y = x^(2) + 3x + 4 `
    D
    `y = x^(2) - 3x + 6 `

  • The gradient (slope) of a curve at any point (x,y) is (x^(2) -4)/(x^(2)) . If the curve passes through the point (2,7) , then the equation of the curve is. . . .

    A
    `y = x + (4)/(x) + 3`
    B
    `y = x + (4)/(x) + 4`
    C
    `y = x^(2) + 3x = 4`
    D
    `y = x^(2) - 3 x + 6`

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    The graph of the function y = f(x) passing through the point (0, 1) and satisfying the differential equation (dy)/(dx) + y cos x = cos x is such that

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