Question

Using a directrix of y = -2 and a focus of (1, 6), what quadratic function is created?

Answer 1

the distance between the vertex and focus is called the focal length and the letter, focal length = a.

the distance between the directrix and focus is 2a... so you know the distance between y = 2 and y = 6

so 2a = 6 - 2

or a = 2

the vertex has the same line of symmetry as the focus

x = 1 and the y value is y = 6 - a or y = 4

so the vertex of the parabola is (1, 4)

the general form of the parabola is

\[(x - h)^2 = 4a(y - k)\]

where (h, k) is the vertex and a is the focal length

use the information above to get the equation

Answer 2

directrix of y = -2 and a focus of (1, 6),

Alternatively, the DEFINITION of a parabola is a locus of points equidistant from a given point (the focus) and a given line (directrix)

All points, (x,y), such that:
Distance from Focus: \(\sqrt{(x-1)^{2}+(y-6)^{2}}\)
Distanced from Directrix: \((y+2)\)

You're almost done!

Answer 3

campbellst is right

Answer 4

AS luck would have it, so is TKHunny! What's the chance of that happening?