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4-4 coordinate system and parameter equation in mathematics elective course
. (Ⅰ) .

(Ⅱ) .?

This exam mainly examines the application of parametric equation and polar coordinate equation. By using the mutual conversion between polar coordinates and rectangular coordinates, and the mutual conversion between parametric equations and rectangular coordinates, a conclusion is drawn.

(1) Use the geometric meaning of the parameter t in the parametric equation of a straight line to find the length of the chord AB.

(2) According to the coordinates of the easily obtained points in the plane rectangular coordinate system, the parameters corresponding to the midpoint can be obtained as follows. According to the nature of midpoint coordinates and the geometric meaning of t, a conclusion is drawn.

Solution:

(1) Substitute the coordinates corresponding to the parameter equation of a straight line into the curve equation for simplification.

If is and the corresponding parameter is; otherwise,. -Three points.

So ... ? -Five points.

(2) The coordinates of the easily obtained point in the plane rectangular coordinate system are, and the parameters corresponding to the midpoint can be obtained according to the properties of the midpoint coordinates. -Eight points.

Therefore, in the geometric sense, the distance from point to point is

. ? -10 point