抛物线y^2=2px(p>0)上有A(x1,y1)B(x2,y2)C(x3,y3)三点,F是它的焦点若|AF|,|BF|
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抛物线y^2=2px(p>0)上有A(x1,y1)B(x2,y2)C(x3,y3)三点,F是它的焦点若|AF|,|BF|,|CF|成等差数列,则()
A.2 x2 = x1 + x3
B.2 y2 = y1 + y3
C.2 x3 = x1 + x2
D.2 y3 = y1 + y2
A.2 x2 = x1 + x3
B.2 y2 = y1 + y3
C.2 x3 = x1 + x2
D.2 y3 = y1 + y2
![抛物线y^2=2px(p>0)上有A(x1,y1)B(x2,y2)C(x3,y3)三点,F是它的焦点若|AF|,|BF|](/uploads/image/z/44238-30-8.jpg?t=%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D2px%EF%BC%88p%EF%BC%9E0%29%E4%B8%8A%E6%9C%89A%28x1%2Cy1%29B%28x2%2Cy2%29C%28x3%2Cy3%29%E4%B8%89%E7%82%B9%2CF%E6%98%AF%E5%AE%83%E7%9A%84%E7%84%A6%E7%82%B9%E8%8B%A5%7CAF%7C%2C%7CBF%7C)
根据抛物线的第二定义可知:|AF|=x1+p/2;|BF|=x2+p/2;|CF|=x3+p/2.
又|AF|,|BF|,|CF|成等差数列,可知|AF|+|CF|=2|BF|,即2 x2 = x1 + x3.
故应选A.
又|AF|,|BF|,|CF|成等差数列,可知|AF|+|CF|=2|BF|,即2 x2 = x1 + x3.
故应选A.
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