Thread: 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

Originally Posted by deltaxray

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 ...

, 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