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Mathematical conic problems in college entrance examination
Analysis: (1) The equation of trajectory c of moving point M can be obtained by directly simplifying the conditional expression given by the topic;

(2) After analysis, when the slope of the straight line M does not exist, it does not satisfy that A is the midpoint of PB. Then the oblique equation of the straight line m is established, combined with the elliptic equation, and then arranged. Write x 1+x2, x 1x2 by using the relationship between roots and coefficients, and get the equation about k by combining 2x 1=x2, so that the slope of the straight line m can be obtained.

Solution: (i) The distance from point M(x, y) to straight line x=4 is twice that from point n (1, 0) to straight line x = 4, then. . . . . .

The trajectory of the moving point m is an ellipse, and the equation is

x2

four

+

y2

three

= 1

(2) p (0 0,3), let A(x 1, y 1) and B(x2, y2), let a be the midpoint of PB, and get 2x 1=0+x2, 2y 1 = 3+y2.

The coordinates of the upper and lower vertices of the ellipse are (0,

three

) and (0,?

three

), the straight line m does not pass through these two points, that is, the slope k of the straight line m exists.

Let the equation of straight line m be: y = kx+3.

. . . . . . . . .

The slope k of the straight line m =+/-.

three

2

.