已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线方程、焦点...已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线
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![已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线方程、焦点...已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线](/uploads/image/z/11424502-46-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E6%96%B9%E7%A8%8B%E4%B8%BAy%5E2%3D2px%28p%3E0%29F%E4%B8%BA%E5%AE%83%E7%9A%84%E7%84%A6%E7%82%B9.%E7%9B%B4%E7%BA%BF2x-y%3D0%E6%88%AA%E6%8A%9B%E7%89%A9%E7%BA%BF%E6%89%80%E5%BE%97%E5%BC%A6%E9%95%BF%E4%B8%BA%E6%A0%B9%E5%8F%B75%2C%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BF%E6%96%B9%E7%A8%8B%E3%80%81%E7%84%A6%E7%82%B9...%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E6%96%B9%E7%A8%8B%E4%B8%BAy%5E2%3D2px%28p%3E0%29F%E4%B8%BA%E5%AE%83%E7%9A%84%E7%84%A6%E7%82%B9.%E7%9B%B4%E7%BA%BF2x-y%3D0%E6%88%AA%E6%8A%9B%E7%89%A9%E7%BA%BF%E6%89%80%E5%BE%97%E5%BC%A6%E9%95%BF%E4%B8%BA%E6%A0%B9%E5%8F%B75%2C%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BF)
已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线方程、焦点...已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线
已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线方程、焦点...
已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线方程、焦点坐标、准线方程
已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线方程、焦点...已知抛物线的方程为y^2=2px(p>0)F为它的焦点.直线2x-y=0截抛物线所得弦长为根号5,求抛物线
将y=2x代入y^2=2px:
4x^2=2px
2x(2x-p)=0
x1=0,x2=p/2
y=2x
y1=0,y2=2*p/2=p
√(x2^2+y2)^2=√5
(p/2)^2+p^2=5
p^2=4
p=2
抛物线方程y^2=4x
焦点坐标(1,0)
准线方程x=-1
设抛物线 与直线的交点为A(x1,y1),B(x2,y2)
由y=2x带入y^2=2px化简得4x^2-2px=0
x1+x2=2p/4=p/2,x1*x2=0
|AB|^2=(1+k^2)[(x1+x2)^2-4x1*x2]=(1+4)[p^2/4-0}=5
得p=2
所以抛物线方程为y^2=4x
将y=2x代入y^2=2px:
4x^2=2px
2x(2x-p)=0
x1=0,x
y1=0,y2=2*p/2=p
√(x2^2+y2)^2=√5
(p/2)^2+p^2=5.抛物线方程y^2=4x
焦点坐标(1,0)
准线方程x=-1 .0