How to draw an ellipse using the second definition of ellipse in Geometry Sketchpad

In recent years, with the rapid development of the mobile game market, the graphics of various games have become more and more beautiful. Among them, elliptical drawing board drawing has become one of the common canvas tools in games with beautiful graphics. What troubles many players is that the drawing of elliptical drawing boards has always been a technical difficulty, but it doesn't matter. PHP editor Banana has prepared a detailed ellipse drawing tutorial for everyone, hoping to help all players master the skills of ellipse drawing. In order to better express the various wonderful forms in the game screen. The following is the detailed operation method of ellipse drawing organized by PHP editor Banana for your reference.

The second definition of ellipse: Assume that the ratio of the distance between the moving point M (x, y) and the fixed point F (c, 0) and the distance from it to the fixed straight line l: x=a2/c is a constant ( a>c>0), then the trajectory of point M is an ellipse. Point F is a focus of the ellipse, and the straight line l is the directrix in the ellipse corresponding to the focus F. The specific operation of constant e=c/a(0 is as follows:

After opening the geometric drawing board, use the [Point Tool] to draw any point F, and use the [Line Tool] to draw a straight line L (the point F is not on L ). Draw a straight line through point F and pick a point P on the straight line.

## Select points F and P and execute the [Measure]-[Distance] command to measure the length of FP; For the length of point F and measured FP, execute [Construction] - [Draw a circle with center and radius] to construct a circle with point F as the center and FP as the radius. Create a new parameter e=0.8 (can be changed to other positive values ​​less than 1). number), calculate the value of FP/e.

Draw a perpendicular to straight line L through point P, intersecting straight line L and point M; with M as the center of the circle, the value of FP/e is Draw a circle with the radius, intersect the perpendicular line at point N, draw a parallel line of straight line L through N, intersect circle F at two points A and B

Select two points A and B, and execute. [Display] - [Track Intersection] command, select the point P with the mouse and drag the point P to move on the straight line PF to get the ellipse equation, and the ellipse is obtained, as shown in the figure

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# Tips: No matter where point P is, it can always be guaranteed that the ratio of the distances from points A and B to point F and their distance to straight line L is 0.8, so the above method is based on the second definition of ellipse.

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