ind an equation for the parabola that has its vertex at the origin and satisfies the given condition. focus F = (0,-1/2)?
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2015-09-16 9:58 am
✔ 最佳答案
F = (0,-1/2) , vertex at the origin , sothe Directrix is : y = 1/2
Let L be y = 1/2
Suppose P(x,y) is a point on the parabola, then
d(P,L) = PF
1/2 - y = √ [ x^2 + ( y + 1/2 )^2 ]
1/4 - y + y^2 = x^2 + ( y + 1/2 )^2
1/4 - y + y^2 = x^2 + y^2 + y + 1/4
2y = - x^2
y = - (1/2)x^2 ... Ans
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