# 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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- LopezLv 54 years agoBest Answer
F = (0,-1/2) , vertex at the origin , so

the 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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