depth of Parabola

Hey guys,

the shape in the image is a cuttout from a paraboloid. I am now trying to calculate the biggest depth of the shape. This does not occur in the centre of the curve since the curve profile is an offset part of a parabola. Anyone have any ideas on how to calculate the biggest depth of the curve and where it occurs.

just a note - the gradient of the tangent of the curved profile at this point should be the same straight line shown in the image which goes from one edge of the curved profile to the other edge.

Any ideas?