For the parabola# x-3 = 1/8 (y+5)^2#, what are the coordinates of the vertex and focus and directrix?
First off, we should recognize that this graph opens to the right. This will be important later. To find the vertex, find the
Next, let's find the focus and directrix. First, though, we should find
To find the focus, we need to start from the vertex. Since the focus is always on the axis of symmetry within the parabola, and since the parabola opens to the right, we need to move
Finally, the directrix will be