Which equation represents a parabola with a focus of (0 4 and a directrix of y=2?

answer: 1/16y^2

step-by-step explanation: youre welcome

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a parabola with a focus of (0,4) and a directrix of y = 2 is sketched as follows: by inspection, it is determined that the vertex of the parabola is (0,3). it is also evident that the distance, p, between the vertex and the focus is 1. it is possible to use the formula (x − h) 2 = 4p(y − k) to derive the equation of the parabola as follows: (x − 0)2 = 4(1)(y − 3) x 2 = 4y − 12 x 2 + 12 = 4y x 2 4 + 3 = y or a point (x,y) on the parabola must be the same distance from the focus as it is from the directrix. for any such point (x,y), the distance to the focus is (x − 0)2 + (y − 4)2 and the distance to the directrix is y − 2. setting this equal leads to: x 2 + y 2 − 8y + 16 = y 2 − 4y + 4 x 2 + 16 = 4y + 4 x 2 4 + 3 = y