The skill of solving the elliptic standard equation in senior high school is how to identify whether the focus is on the X axis or the Y axis through the elliptic standard equation. First, determine which axis the denominators of X and Y are on, then the denominator of X is the square of the semi-long axis, and the denominator of Y is the square of the semi-short axis.

An ellipse is a set of points on a plane, and the sum of their distances to two given points is constant. These two fixed points are called the focus of the ellipse. Ellipse has a magical property: choose any point P on the ellipse to connect with two focal points A and B, then PA and PB have the same included angle with the tangent of the ellipse at point P, in other words, the included angle between PA and PB and the normal is equal, that is, the incident angle is equal to the reflection angle.

Optical solutions:

Explain by Fermat's principle (light always travels along the shortest path). We need to prove a geometric proposition: a point P on the ellipse is equal to the angle formed by the tangent line connecting the focal points A and B of the point P.. After the tangent passes through point P, we can see that the assertion that A- > looks at it is correct: the light at point A passes through point B after being reflected by the tangent, so the reflection point must be point P, because all other points on the tangent P' are outside the ellipse, and the dotted line A->; p '-& gt； B is better than A-> p->； B it's very long.