Question

Find the standard form of the equation of the parabola with a focus at (0, 4) and a directrix at y = -4. Answer choices: y = 1/16x2 y2 = 16x y2 = 4x y = 1/4x2

Answer 1

a) The standard form of the equation

`y=(16)/(x^(2) )`

Explanation:

Explanation:-

A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane

• The Fixed line is called the directrix of the parabola.

• The Fixed point is called the focus of the parabola.

• A line through the focus and perpendicular to the directrix is called the axis of the parabola.

• The point of intersection of parabola with the axis is called the vertex of the parabola.

Given Focus of the parabola S(0,a)= (0,4)

Given Focus is lies on y-axis and the directrix is parallel to x-axis

Given directrix of the parabola y = -4

Directrix y = -a

Standard form of the parabola

x² = 4ay

x² = 4(4)y

x² = 16y

`y=(16)/(x^(2) )`