Question

T he equation for a parabola with directrix y = –p and focus (0, p) is:

1.What is the parabola’s line of symmetry?

y-axis
x-axis
x = p
x = -p

Answer 1

The parabola with directrix y = -p and focus (0, p) is symmetrical about the y-axis.

Step-by-step explanation:

The equation for a parabola can be determined using the position of the directrix and the focus. Given the directrix y = -p and the focus at (0, p), the parabola is symmetrical about the axis that is equidistant from the directrix and the focus. As the directrix is a horizontal line and the focus has a y-coordinate that is just an equal distance from the x-axis on the opposite side, this axis of symmetry must be the vertical line that goes through the focus, which is the y-axis.

Answer 2

The equation for a parabola with directrix y = –p and focus (0, p)

The distance between vertex and directrix is P

Also the distance between vertex and focus is also P

Focus (0,p) so focus lies on y axis

Directrix line is paralled to focus point

So Directex crosses the x axis .

Hence line of symmetry lies is the y-axis.

The graph is attached below.