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解:(1)直線與軸交于點.與軸交于點. .······························································································· 1分 點都在拋物線上. 拋物線的解析式為······························································ 3分 頂點····································································································· 4分 (2)存在····················································································································· 5分 ··················································································································· 7分 ·················································································································· 9分 (3)存在···················································································································· 10分 理由: 解法一: 延長到點.使.連接交直線于點.則點就是所求的點. ··························································································· 11分 過點作于點. 點在拋物線上. 在中.. .. 在中.. ..····················································· 12分 設直線的解析式為 解得 ······································································································ 13分 解得 在直線上存在點.使得的周長最小.此時.········· 14分 解法二: 過點作的垂線交軸于點.則點為點關于直線的對稱點.連接交于點.則點即為所求.···················································································· 11分 過點作軸于點.則.. . 同方法一可求得. 在中...可求得. 為線段的垂直平分線.可證得為等邊三角形. 垂直平分. 即點為點關于的對稱點.··················································· 12分 設直線的解析式為.由題意得 解得 ······································································································ 13分 解得 在直線上存在點.使得的周長最小.此時. 1 查看更多

 

題目列表(包括答案和解析)

已知:直線軸交于A,與軸交于D,拋物線與直線交于A、E兩點,與軸交于B、C兩點,且B點坐標為 (1,0).

(1)求拋物線的解析式;

(2)動點P軸上移動,當△PAE是直角三角形時,求點P的坐標.

(3)在拋物線的對稱軸上找一點M,使的值最大,求出點M的坐標.

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已知:如圖,拋物線軸交于點,與軸交于點A、B,點A的坐標為(4,0)

1.求該拋物線的解析式;

2.點Q是線段AB上的動點,過點Q作QE//AC,交BC于點E,連接CQ,設△CQE的面積為S,Q(m,0),試求S與m之間的函數關系式(寫出自變量m的取值范圍);

3.在(2)的條件下,當△CQE的面積最大時,求點E的坐標.

4.若平行于x軸的動直線l與該拋物線交于點P,與直線AC交于點F,點D的坐標為(2,0). 問:是否存在這樣的直線l,使得△ODF是等腰三角形?若存在,請求出點P的坐標,若不存在,請說明理由.

 

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已知:如圖,拋物線軸交于點,與軸交于點A、B,點A的坐標為(4,0)

1.求該拋物線的解析式;

2.點Q是線段AB上的動點,過點Q作QE//AC,交BC于點E,連接CQ,設△CQE的面積為S,Q(m,0),試求S與m之間的函數關系式(寫出自變量m的取值范圍);

3.在(2)的條件下,當△CQE的面積最大時,求點E的坐標.

4.若平行于x軸的動直線l與該拋物線交于點P,與直線AC交于點F,點D的坐標為(2,0). 問:是否存在這樣的直線l,使得△ODF是等腰三角形?若存在,請求出點P的坐標,若不存在,請說明理由.

 

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直線y=k1x+b與雙曲線y=
k2x
只有一個交點A(1,2),且與x軸、y軸分別交于B、C兩點,AD垂精英家教網直平分OB,垂足為D,求:
(1)直線、雙曲線的解析式;
(2)線段BC的長;
(3)三角形BOC的內心到三邊的距離.

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直線y=k1x+b與雙曲線y=
k2x
只有一個交點A(1,2),且與x軸、y軸分別交于B、C兩點,AD垂直平分OB,垂足為D.求:
(1)直線、雙曲線的解析式.
(2)線段BC的長.

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