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Math Help - parabola and tangent

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    parabola and tangent

    Find the equation of the parabola: vertex at (3,-1), axis parallel to the y- axis and the line 4x + y - 7= 0 is a tangent

    Thanks
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    Quote Originally Posted by deltaxray View Post
    Find the equation of the parabola: vertex at (3,-1), axis parallel to the y- axis and the line 4x + y - 7= 0 is a tangent

    Thanks

    given the vertex and direction of the axis of symmetry, the equation of the parabola is ...

    y = a(x-3)^2 - 1 , where a is a constant TBD.


    since the line y = -4x+7 is tangent to the parabola ...

    (1) the line and parabola are equal at the point of tangency

    a(x-3)^2 - 1 = -4x+7

    (2) the slope of the parabola at the point of tangency equals the slope of the line

    2a(x-3) = -4


    solve the system of equations for x and a
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