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Determine the quadratic curve y=f(x) if ...

Determine the quadratic curve `y=f(x)` if it touches the line `y=x` at the point `x=1` and passes through the point `(-1,0)dot`

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Knowledge Check

  • If the line y=2x touches the curve y=ax^(2)+bx+c at the point where x=1 and the curve passes through the point (-1,0), then

    A
    `a=(1)/(2), b=1, c=(1)/(2) `
    B
    `a=1, b=(1)/(2), c=(1)/(2) `
    C
    `a=(1)/(2), c=(1)/(2), b=1 `
    D
    none of these

  • The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

    A
    `(4/3,2e)`
    B
    (2, 3e)
    C
    `(5/3,2e)`
    D
    (3, 6e)

  • Equation of the curve whose slope at the point (x,y) is -(x + y) / x and which passes through the points (2, 1) is

    A
    `2y^(2)+xy=4`
    B
    `y^(2)+xy=3`
    C
    `x^(2)+2xy=8`
    D
    None of these

    • Similar Questions

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    The line y = x is a tangent to the curve y=px^(2)+qx+r at the point x =1. If the curve passes through the point (-1, 0) then the value of (p+r)/q is

    Find the equation of the line through the point of intersection of x+2y=5 and x-3y=7 and passing through the point (0, -1)

    The tangent to the curve y=x^(2)-5x+5 . parallel to the line 2y=4x+1, also passes through the point:

    If y=f(x) be the equation of a parabola which is touch by the line y=x at the point where x=1 then

    The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, -3). Then its radius is 0

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