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在初三复习教学中,下面两道中考题引起了笔者的注意:试题1(2008南通)如图1,已知双曲线y=k/x与直线y=1/4x相交于A,B两点.第一象限上的点M(m,n)(在A点左侧)是双曲线y=k/x上的动点.过点B作BD//y轴交x轴于点D.过N(0,-n)作NC//x轴交双曲y=k/x于点E,交BD于点C.(1)若点D坐标是(-8,0),求A,B两点坐标及k的值.(2)若B是CD的中点,四边形OBCE的面积为4,求直线CM的解析式.
In the junior high school reviewing teaching, the following two exam questions aroused the author’s attention: Test 1 (2008 Nantong) shown in Figure 1, known hyperbolic y = k / x and y = 1 / 4x straight line intersects at A, B The point M (m, n) on the first quadrant (to the left of point A) is the point of motion on the hyperbola y = k / x. N (0, -n) for NC // x-axis hyperbolic y = k / x at point E, cross BD at point C. (1) If the point D coordinate is (-8,0), find A, B Coordinates of two points and the value of k. (2) If B is the midpoint of the CD, quadrilateral OBCE area of 4, find a straight line CM analytic formula.