(1) Find the standard equation of ellipse;

(2) The straight line intersects with the ellipse at two points, and intersects with the vertical line. The vertical feet are respectively, and the point is the midpoint of the line segment and the left focus of the ellipse.

Answer the question 1

Elliptic intersection

The standard equation of ellipse is:

Answer question 2

According to the conclusion in the previous section,

The focus on the left is,

The straight line passes through the point, which is focus chord;

Remember that the inclination of a straight line is, then

Substituting the numerical value can get:

∴

∴

∴

∵ A straight line is parallel to the axis, a straight line is not parallel to the axis, and a straight line is not parallel.

A quadrilateral is a trapezoid. Prove completion.

Refine and improve

The straight line passes through the point, which is focus chord; It is more effective to solve this problem with elliptic polar coordinate equation.