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dusya [7]
3 years ago
10

Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. F(–2, 0);

x = 2
Mathematics
1 answer:
UNO [17]3 years ago
8 0
The line is called the directrix.  Here we have a vertical directrix, so a parabola sideways from usual.

Geometry is best done with squared distances.  The squared distance from an arbitrary point (x,y) to the vertical line x=2 is (x-2)^2.

We equate that to the squared distance of (x,y) to the focus (-2,0): 

(x-2)^2 = (x - -2)^2 + (y - 0)^2

x^2 -4x + 4=x^2 +4x +4 + y^2

-8x = y^2

We could call that done.  A more standard form might be

x =- \dfrac 1 8 \ y^2

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