Question

The Directrix of a parabola is y=2. Its focus is (4,-4).

What is the equation of the parabola in vertex form?
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y= (x- )^2 - .

Answer 1

The equation of the parabola in vertex form is y = (3/4)(x-4)^2 - 4.

Step-by-step explanation:

The equation of a parabola in vertex form is given by

y = a(x-h)^2 + k,

where (h,k) represents the coordinates of the vertex.

The vertex of the parabola is given by the point (h, k) = (4, -4). So, the equation becomes

y = a(x-4)^2 - 4.

The directrix of the parabola is y = 2.

The distance between the vertex and the directrix is equal to the distance between the vertex and the focus. Hence, the value of 'a' can be determined as follows:

(4-4)^2 + (-4-2) = a(2*(-4))

Simplifying the equation, we get -6 = -8a, which leads to a = 3/4.

Substituting the value of 'a' in the equation, we get the equation of the parabola as

y = (3/4)(x-4)^2 - 4.