Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 2? x2=−4y x2=−y x2=−4(y−1) x2=−(y−1)
Mathematics · Middle School · Tue Nov 03 2020
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The general equation of the parabola that has a focus on(x',y') is
√[(x-x')^2+(y-y')^2] distance formula….(A)
Using the general distance formula for the given question at the focus point (0,0) distance will be √[(x-0)^2+(y-0)^2]
√[x^2+y^2]……(1)
In question the distance between (x,y) and the directrix y = 2, from(x, y)….
Distance (y-2)…..(2)
Both distances are equal in a parabola so equation(1)=(2)
√[x^2+y^2]=(y-2)
By doing square on both side
[x^2+y^2]=(y-2)^2
x^2+y^2=y^2+4-4y
x^2+y^2-y^2-4+4y=0
x^2-4+4y=0
x^2=4(1-y)
x^2=-4(y-1)
the equation represents a parabola that has a focus of (0, 0) and a directrix of y = 2 is
x^2=-4(y-1) answer.