已知直线与抛物线y²=2px(p>0)交于A,B两点,且OA⊥OB,OD⊥AB交AB与点D(1)求点D的轨迹方程(2)若点D坐标为(2,1)求P的值
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![已知直线与抛物线y²=2px(p>0)交于A,B两点,且OA⊥OB,OD⊥AB交AB与点D(1)求点D的轨迹方程(2)若点D坐标为(2,1)求P的值](/uploads/image/z/12384310-22-0.jpg?t=%E5%B7%B2%E7%9F%A5%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFy%26sup2%3B%3D2px%28p%3E0%29%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%94OA%E2%8A%A5OB%2COD%E2%8A%A5AB%E4%BA%A4AB%E4%B8%8E%E7%82%B9D%281%29%E6%B1%82%E7%82%B9D%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B%282%29%E8%8B%A5%E7%82%B9D%E5%9D%90%E6%A0%87%E4%B8%BA%282%2C1%29%E6%B1%82P%E7%9A%84%E5%80%BC)
已知直线与抛物线y²=2px(p>0)交于A,B两点,且OA⊥OB,OD⊥AB交AB与点D(1)求点D的轨迹方程(2)若点D坐标为(2,1)求P的值
已知直线与抛物线y²=2px(p>0)交于A,B两点,且OA⊥OB,OD⊥AB交AB与点D
(1)求点D的轨迹方程
(2)若点D坐标为(2,1)求P的值
已知直线与抛物线y²=2px(p>0)交于A,B两点,且OA⊥OB,OD⊥AB交AB与点D(1)求点D的轨迹方程(2)若点D坐标为(2,1)求P的值
设A(a^2/(2p),a),B(b^2/(2p),b),D(x,y)
OA⊥OB
a/(a^2/(2p)*b/(b^2/(2p)=-1
ab=-4p^2
OD⊥AB
y/x*(a-b)/[(a^2-b^2)/(2p)]=-1
y/x=-(a+b)/(2p)
点D在直线AB上
y-a=(a-b)/[(a^2-b^2)/(2p)][(x-a^2/(2p)]
(a+b)(y-a)=2px-a^2
(a+b)y-ab=2px
-2py/x*y+4p^2=2px
x^2-2px+y^2=0
点D的轨迹方程是(x-p)^2+y^2=p^2
(2)若点D坐标为(2,1),4-4p+1=0
p=5/4