Write an equation for the parabola with focus at (0, -2) and directrix x = 2.

Solution:

Given,

Focus at (0, -2), directrix x = 2.

Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

As a plane curve, it may be defined as the path (locus) of a point moving so that its distance from a fixedline(the directrix) is equal to its distance from a fixed point (the focus).

The equation of the parabola with focus and directrix - F(a, b), D(y = c) is given by

(x - a)² + b² - c² = 2y(b - c)

Substitute F(0, -2) and D(x, 2) ∀ x:y(x) = c

x² - 2y(2 - (-2) ) = -8y

y = -1/8x².

Therefore, the equation for the parabola is y = -1/8x².

Write an equation for the parabola with focus at (0, -2) and directrix x = 2.

Summary:

Equation for the parabola with focus at (0, -2) and directrix x = 2 is y = -1/8x².