Question

What is the equation of the parabola shown below, given a focus at F(1, 5) and a directrix of x = −3? In addition, identify the vertex and the equation of the axis of symmetry for the parabola.

Answer 1

$\begin{gathered} x=\frac{1}{8}(y-5)^2-1,\text{ vertex :(-1, 5)} \\ \\ \text{axis of symmetry: y=5} \end{gathered}$

EXPLANATION

First, let's find the vertex.

From the graph, the vertex is (-1, 5).

It is symmetric about y = 5

Length of the Latus rectom (a) =2 x 4 = 8

Therefore, the equation of the graph is;

$y=\frac{1}{a}(y-5)^2-1$

Substitute a = 8

$x=\frac{1}{8}(y-5)^2-1$