Question

What is an equation of a parabola with vertex at the origin and directrix y =2.8?​

Answer 1

Answer: B)  y = (-5/56)x^2

Work Shown:

Vertex = (0,0) = (h,k)

directrix is y = 2.8

vertical distance from y = 0 to y = 2.8 is 2.8 units

2.8 = 28/10 = 14/5

p = 14/5 is the focal distance

a = -1/(4*p) = -1/(4*14/5) = -1/(56/5) = -5/56

The value of 'a' is negative because the directrix is above the focus, which means the focal point is below the vertex.

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

y = (-5/56)(x-0)^2 + 0

y = (-5/56)x^2