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

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- Mar 20th 2010, 05:14 AMdeltaxrayparabola 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 - Mar 20th 2010, 06:46 AMskeeter

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

, where is a constant TBD.

since the line is tangent to the parabola ...

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

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

solve the system of equations for and