Find the vertex, focus, and directrix of the parabola. y^2= -10x

Answer 1

Put the parabola in the form (y - k)² = 4p(x - h) with (h,k) being the vertex and p being the distance from the vertex to the focus.

We get y² = -10x becomes (y - 0)² = -10(x - 0). h and k are both 0 so the vertex is (0, 0)

4p = -10. Therefore, p = -10/4 or -2.5.

The parabola is horizontal so the focus is 2.5 units to the left of the vertex at the point (-2.5, 0). The directrix is a line 2.5 units in the opposite direction and is a vertical line with x = 2.5. I think it helps to draw out a rough sketch of the parabola first, so you can see approximately where the focus and directrix are.