2010年高考压轴题数学跟踪演练系列六（2010 college entrance examination finale mathematical tracking exercises series six）.docVIP

2010年高考压轴题数学跟踪演练系列六（2010 college entrance examination finale mathematical tracking exercises series six） For the 2010 college entrance examination mathematics -- six series finale title track drill (the only 1. out of 14) Figure, a parabolic F focus point P, moving in a straight line, two lines PA, P for PB parabola C, and C A, respectively the parabola is tangent to B points. (1) the trajectory equation of gravity center G Delta APB. (2) proof / PFA= / PFB. Solution: (1) a point A, B coordinates respectively, The AP equation for the tangent formula: Tangent BP equation: Coordinate solution for p: So the coordinates of the gravity center G for Delta APB, So, from the point of P on line L movement, to obtain the trajectory equation for gravity center G: Methods 1 (2): because Because P in parabola, then L Similarly there L / AFP= / PFB. Method 2: when p is p so coordinates, distance to the line AF: That is So the distance P to the line BF: So d1=d2 / AFP= / PFB., i.e. The linear equation was AF: Linear BF equation: So the distance P to the line AF: Similarly, available P to a straight line distance of BF, thus can be obtained by d1=d2 / AFP= / PFB.. (the only 2. out of 12) Let A and B are two points on the ellipse, N (1, 3) is the midpoint of the line AB, AB line perpendicular bisector and ellipse intersect at C and D points. (I) determine the range, and for linear AB equation; (II) test to determine whether there is such that A, B, C, D, four points in the same circle? And explain the reason. (this does not require drawing on the sheet) This text mainly examines the basic knowledge of straight line, circle and ellipse plane analytic geometry and reasoning ability and comprehensive solution to the problem. (I) 1 solutions: according to the meaning of problems, a linear AB equation, finishing 1. Let be two different root of equation, Star II And by N (1, 3) is the midpoint of the line AB, too Solution of k= 1, the substitution, the range is (12 + 2). Then, the linear