Question

Writing an equation of a probably given the vertex and focus

Answer 1

The equation of the vertical parabola in vertex form is written as

$y=\frac{1}{4p}(x-h)^2+k$

Where (h, k) are the coordinates of the vertex and p is the focal distance.

The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.

$p=1-6=-5$

Using this value for p and (3, 1) as the vertex, we have our equation

$y=-\frac{1}{20}(x-3)^2+1$