Current location - Training Enrollment Network - Mathematics courses - The last problem of mathematics in Shenzhen senior high school entrance examination in recent years
The last problem of mathematics in Shenzhen senior high school entrance examination in recent years
Is this from 2009? The picture shows the screenshot of the answer! ?

22.(9 o'clock) As shown in the figure, in the rectangular coordinate system, the coordinate of point A is (-2,0), connect OA, and rotate the line segment OA clockwise around the origin o 120 to get the line segment OB.

(1) Find the coordinates of point B;

(2) Find the analytical formula of parabola passing through points A, O and B;

(3) Is there a point C on the axis of symmetry of the parabola in (2) that minimizes the circumference of △BOC? If it exists, find the coordinates of point C; If it does not exist, please explain why.

(4) If point P is the moving point on the parabola in (2) and below the X axis, is the area of △PAB the largest? If yes, calculate the coordinates of point P and the maximum area of delta delta △PAB at this time; If not, please explain why.

23. As shown in the figure, in the plane rectangular coordinate system, the straight line L: Y =-2x-8 intersects the X axis and the Y axis at two points A and B respectively, and the point P(0, k) is a moving point on the negative semi-axis of the Y axis, with P as the center and 3 as the radius.

(1) Connect PA, if PA=PB, try to judge the position relationship between ⊙P and X axis, and explain the reasons;

(2) When k is what value, is the triangle whose vertex is ⊙P and the intersection of straight line L and center p a regular triangle? ?

Download the test paper here:/view/7F803669A45177232F60A2ae.html.