Question

A parabola has a directrix of y=1 and a focus of (1,12). Which statement is true?A)The parabola opens upward.B)The parabola opens downward.C)The parabola opens to the left.D)The parabola opens to the right.

Answer 1

1) Since the directrix is y=1 and the focus (1,12) We can write that, using the distance formula:

$\begin{gathered} \sqrt[]{(y-1)^2}=\sqrt[]{(x-1)^2+(y-12)^2} \\ (y-1)^2=(x-1)^2+(y-12)^2 \\ y^2-2y+1=x^2-2x+1+y^2-24y+144 \\ -2y+1=x^2-2x+1-24y+144 \\ -2y+24y=x^2-2x+145 \\ -22y=x^2-2x+145 \\ y=\frac{x^2-2x+145}{22} \\ \\ y=\frac{x^2-2x+145}{22} \end{gathered}$

2) Then we can state that the correct option is A the parabola opens upward.