25. It is known that ⊙T and the coordinate axis have four different intersections M, P, N and Q, where P is the intersection of a straight line and the axis, and point Q and point P are symmetrical about the origin. The parabola passes through points m, p and n, and its vertex is H.

(1) Find the coordinates of point Q;

(2) Point out which straight line the center of the circle T must move on;

(3) When point H is on a straight line, and the radius ⊙T is equal to the distance from the center of the circle t to the origin, can we determine the value of? If yes, request a value; If not, please explain why. (Figure 25 is for analysis and reference)

25. As shown in the figure, point A (0, 1) and point C (4, 3) are known, point P is a moving point in the rectangular ABCD with AC as the diagonal (not on each side), point D is on the Y axis, and the parabola has p as the vertex.

(1) means that points A, C and E are on a straight line;

(2) Can we judge the opening direction of parabola? Please explain the reasons;

(3) If the parabola and the X-axis have intersections F and G(F is on the left side of G), the area difference between △GAO and △FAO is 3, and the parabola and the line segment AE have two different intersections, can the values of A and B be determined? If yes, request the values of a and b; If not, please determine the range of a and b.

(The figures in this question are for analysis and reference only. )

25. as shown in figure 1, point a is the moving point of a straight line y = kx (k > 0, k is constant), a parabola with vertex y = (x-h) 2+m intersects with the straight line y = x at another point e, the y axis is at point f, the parabola symmetry axis is at point b and the straight line EF is at point C ..

(1) Please write the relationship between H and M; (represented by the included k formula)

(2) When point A moves to make EF parallel to the X axis (as shown in Figure 2), find the ratio OF line segment AC to of;

(3) When point A moves to the lowest position OF point F (as shown in Figure 3), find the ratio of line segment AC to of.

2008)

25. As shown in figure 1, the coordinates of three vertices in quadrilateral OABC are known as O (0 0,0), A (0 0,n) and C (m m,0). The moving point P starts from the point O and moves to the point C along the lines OA, AB and BC in turn. Let the moving distance be z, and the image of OPC area s changing with z is shown in Figure 2. m..

(1) Please determine the value of n and the coordinates of point B;

(2) When the moving point P is the vertex of the parabola Y = AX+BX+C passing through points O and C, and it is on the hyperbola Y =, find the area of the quadrilateral OABC at this time.

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What was discovered in 2005 and 2006 was all from the curriculum reform area! Your teacher should have!