圓與圓錐曲線的一些公式

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 點P(x₀,
y₀)與圓的相關位置
                
            

        

                    
                
                
            

        

平面上一點P(x₀, y₀)與圓的相關位置的判斷如下：
                
            

        

1.若
                P在圓內
                    
                
                    
                
                
            

        

2.若
                P在圓上
                    
                
                    
                
                
            

        

3.若
                P在圓外
                    
                
                    

        

　

        

                
                
            

        

  

        

　

        

                
            

        

圓與直線的關係
                    
                

        

直線L : ax + by + c = 0；圓C：
                    
                  (r     
> 0)，
                
            

        

                    
                
                
            

        

相離：d > r
                
                
            

        

相切：d = r
                    
                

        

相割：d < r
                
            

        

          

        

        

                
            

        

 拋物線的名詞
                
            

        

(1)對稱軸：過焦點垂直準線的直線。
                
            

        

(2)頂點：拋物線與對稱軸相交的點。
                
            

        

(3)焦距：焦點與頂點的距離。
                
            

        

(4)弦：拋物線上任意兩點的連線段。
                
            

        

(5)焦弦：通過焦點的弦。
                
            

        

(6)正焦弦：垂直對稱軸的焦弦。

[此贴子已经被作者于2008-8-28 16:33:11编辑过]

teddylydia

 

                
            

        

 拋物線的標準方程式 
                
            

        
    
        
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
        

方程式	y2 = 4cx
對稱軸	y = 0	y = k
頂點	(0, 0)	(h, k)
焦點	(c, 0)	(c + h, k)
準線	x = -c
正焦弦長

    
        

 
                
            

        
    
        
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
        

方程式
對稱軸		x = k
頂點	(0, 0)	(h, k)
焦點	(0, c)	(h, c + k)
準線
正焦弦長

    
        

                                                       

                
            

        

 
                
            

        

 橢圓的名詞
                
            

        

(1)對稱中心：兩焦點所連線段
                    
            的中點，亦即兩對稱軸交點。
                
            

        

(2)頂點：橢圓圖形與兩對稱軸的交點。
                
            

        

(3)長軸：直線
                    
            與圖形交點的連線段
                    
            。
                
            

        

(4)短軸：過中心垂直長的直線與圖形交點所連線段
                    
            。
                
            

        

(5)弦：橢圓上任意兩點所連線段。
                
            

        

(6)焦弦：通過焦點的弦。
                
            

        

(7)正焦弦：垂直長軸的焦弦。

        

                   
                                                   

        

橢圓的標準方程式
                    
                

        

 
                
            

        
    
        
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
        

橢圓方程式
(1)對稱軸	,	x = h, y = k
(2)對稱中心	(0, 0)	(h, k)
(3)頂點	(                                            , 0), (0,                                               )	(                                            , k),(h,                                                   )
(4)焦點	(                                            , 0)	(                                            ,k), c2       = a2 -                                 b2
(5)長軸長	2a	2a
(6)短軸長	2b	2b
(7)正焦弦長

    
        

 
                
            

        

 
                
            

        
    
        
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
        

橢圓方程式
(1)對稱軸	,	x = h, y = k
(2)對稱中心	(0, 0)	(h, k)
(3)頂點	(                                            , 0), (0,                                               )	(                                            , k),(h,                                                   )
(4)焦點	(0,                                               )	(h,                                            ), c2 = a2       -                                 b2
(5)長軸長	2a	2a
(6)短軸長	2b	2b
(7)正焦弦長

    
        

 
                
            

        

                                             

        

 

teddylydia

雙曲線的名詞
                
            

        

(1)對稱中心：兩焦點所連線段
                    
            的中點，亦即兩對稱軸交點。
                
            

        

(2)頂點：雙曲線圖形與
                    
            相交的點。
                
            

        

(3)貫軸：兩頂點所連成的線段。
                
            

        

(4)共軛軸：過中心而垂直貫軸的直線上取點B,B¢對稱於中心，
                    
            （其中
                    
            ），
                    
            稱為共軛軸。
                
            

        

(5)弦：雙曲線上任意兩點所連線段。
                
            

        

(6)焦弦：通過焦點的弦。
                
            

        

(7)正焦弦：垂直貫軸的焦弦。
                
            

        

(8)焦軸：兩焦點距離。
                
            

        

(9)共軛雙曲線：貫軸、共軛軸互換之兩個雙曲線彼此為共軛雙曲線。
                
            

        

                
            

        

雙曲線的標準方程式
                    
                

        
    
        
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
        

雙曲線方程式
對稱軸	,	x = h, y = k
對稱中心	(0, 0)	(h, k)
頂點	(                                            , 0)	(                                            , k)
焦點	(                                            , 0)	(                                            , k), c2       = a2 -                                 b2
貫軸長	2a	2a
共軛軸長	2b	2b
正焦弦長
共軛雙曲線

    
        

 
                
            

        

 
                
            

        
    
        
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
            
                
                
                
            
        

雙曲線方程式
對稱軸	,	x = h, y = k
對稱中心	(0, 0)	(h, k)
頂點	(0,                                               )	(h,                                            )
焦點	(0,                                               )	(h,                                            ), c2 = a2       -                                 b2
貫軸長	2a	2a
共軛軸長	2b	2b
正焦弦長
共軛雙曲線

    
        

                
            

        

 雙曲線的漸近線
                
            

        
    
        
                
                
            
            
                
                
            
            
                
                
            
            
                
                
            
            
                
                
            
        

雙曲線方程式	雙曲線漸近線
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