Question

How do you find the focus, vertex, and directrix of `y^2=-28x`?

Answer 1

The size-parameter a = 7. Vertex V is (0, 0). Focus S is `(-7, 0)`. Directrix is along x = 7.

Explanation:

Compare with the standard form `y^2=-4ax` representing the mirror image, with respect to y-axis, of the parabola `y^2=4ax`.

a = 7. x-axis, from the vertex V(0, 0,) in the negative direction is the axis of the parabola.

Focus `S(-7, 0)` is on this axis, at a distance a = 7 from the vertex.

The directrix x = a = 7 is perpendicular to the axis of the parabola, at an equal distance, on the other side of the vertex. .