Math Help - ellipse

1.Verify that the line x + 2y = 8 meets the ellipse 3x2 + 4y2 = 48 at exactly one point,
namely P = (2, 3). The line is said to be tangent to the ellipse. Verify also that the focal points for this ellipse are F1 = (−2, 0) and F2 = (2, 0).


2.(Continuation) The reflection property of the ellipse: Use trigonometry to calculate
the size of the acute angle formed by the tangent line and the focal radius F2P. Do the
same for the acute angle formed by the tangent line and the focal radius F1P. How do
your answers to these two calculations explain the title of this problem?


I am not sure about the answer to the second problem.

Originally Posted by Veronica1999

1.Verify that the line x + 2y = 8 meets the ellipse 3x2 + 4y2 = 48 at exactly one point,
namely P = (2, 3). The line is said to be tangent to the ellipse. Verify also that the focal points for this ellipse are F1 = (−2, 0) and F2 = (2, 0).


2.(Continuation) The reflection property of the ellipse: Use trigonometry to calculate
the size of the acute angle formed by the tangent line and the focal radius F2P. Do the
same for the acute angle formed by the tangent line and the focal radius F1P. How do
your answers to these two calculations explain the title of this problem?


I am not sure about the answer to the second problem.

Since the angles between the tangent and the the two focal radii are equal this situation describes a simple optical reflection of a light-ray at the ellipse. For further information have a look here:The Reflective Property of an Ellipse