數(shù)學 A（理）,45分鐘階段測試(十三),第九章 平面解析幾何,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,答案 C,2.設(shè)雙曲線的一個焦點為F，虛軸的一個端點為B，如果直線FB與該雙曲線的一條漸近線垂直，那么此雙曲線的離心率為( ),3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,答案 D,3.已知拋物線關(guān)于x軸對稱，它的頂點在坐標原點O，并且經(jīng)過點M(2，y0).若點M到該拋物線焦點的距離為3，則|OM|等于( ),2,4,5,6,7,8,9,10,1,3,2,4,5,6,7,8,9,10,1,3,答案 B,2,3,5,6,7,8,9,10,1,4,2,3,5,6,7,8,9,10,1,4,2,3,5,6,7,8,9,10,1,4,即橢圓C上有4個點是“”點.,答案 B,5.已知拋物線y22px (p0)，過其焦點且斜率為1的直線交拋物線于A、B兩點，若線段AB的中點的縱坐標為2，則該拋物線的準線方程為( ) A.x1 B.x1 C.x2 D.x2,2,3,4,6,7,8,9,10,1,5,2,3,4,6,7,8,9,10,1,5,得(y1y2)(y1y2)2p(x1x2).,又線段AB的中點的縱坐標為2，即y1y24，,直線AB的斜率為1，故2p4，p2，,答案 B,二、填空題 6.已知拋物線y22px (p0)的準線與圓x2y26x70相切，則p的值為_.,2,3,4,5,7,8,9,10,1,6,圓x2y26x70可化為(x3)2y216，,2,2,3,4,5,6,8,9,10,1,7,2,3,4,5,6,8,9,10,1,7,可得4c2364a2， 即a2c29，故有b3. 答案 3,2,3,4,5,6,7,9,10,1,8,2,3,4,5,6,7,9,10,1,8,2,3,4,5,6,7,9,10,1,8,答案 ,2,3,4,5,6,7,8,10,1,9,2,3,4,5,6,7,8,10,1,9,2,3,4,5,6,7,8,10,1,9,(2)設(shè)直線l過橢圓的焦點且與圓C相切，求直線l的方程.,2,3,4,5,6,7,8,10,1,9,2,3,4,5,6,7,8,9,1,10,解 由已知，得x4不合題意，,設(shè)直線l的方程為yk(x4)，,由已知，得拋物線C的焦點坐標為(1,0)，,2,3,4,5,6,7,8,9,1,10,2,3,4,5,6,7,8,9,1,10,(2)設(shè)A，B為拋物線上兩點，且AB不垂直于x軸，若線段AB的垂直平分線恰過點M，求證：線段AB中點的橫坐標為定值.,證明 設(shè)線段AB中點的坐標為N(x0，y0),A(x1，y1),B(x2，y2)，,2,3,4,5,6,7,8,9,1,10,2,3,4,5,6,7,8,9,1,10,所以x02，即線段AB中點的橫坐標為定值2.,