The focus of a parabola is (0,2), and its directrix is the vertical line x=-6. What is the axis of symmetry, the vertex, and the direction the parabola opens?

Question

This is a math question that I do not understand. How do you get the c value (if focus is h+c and directrix is h-c) and find the equation from there?

Answer 1

the vertex and the focus both lie on the axis of symmetry

the axis of symmetry is y=2

the vertex is equidistant from the focus and the directrix

the distance from the focus to the directrix is 6 units ( half of 6 is 3 )

therefore the vertex is (-3,2)

the vertex is between the directrix and the focus and the directrix is always below the vertex, above the vertex, to the left of the vertex or to the right of the vertex, and the focus is always inside of the parabola, so because the directrix is x=-6, the parabola opens to the right (not to the left, not up, and not down)

Answer 2

Vertex: (-6,2)

Axis of Symmetry: X-axis

The parabola opens towards positive infinity on the x-axis.