The equation of elliptical region is   and the point on edge of the shadow is.

Observe the graph.

The edge of the shadow is tangent to the curve.

Slope of the tangent is derivative of the curve.

Consider equation of ellipse .

Differentiate on each side with respect to .

.

Assume that the ellipse has the tangent at the point .

Slope of the tangent at .

.

Point-slope form of line equation: .

Substitute and in  the above formula.

.

The above line passes through the point .

So it will satisfy the above tangent line equation.

The point lies on ellipse.

Therefore we have, .

Substitute in .

.

.

Substitute in .

Thus the points are and .

The lamp is located in positive - axis direction, so we consider the point  only.

Slope of the tangent at  is .

Point-slope form of line equation: .

Substitute and in  the point-slope formula.

From the graph, it is observe that lamp is located 3-units right from the -axis.

And assume that lamp is located units above -axis.

Thus the coordinates of the point at which lamp is located are .

The tangent line passes through the point .

Hence it will satisfy the line equation.

Therefore, the lamp is situated 2 units above the -axis.

The lamp is situated 2 units above the -axis.