Thee vertex of a parabola is (-5,2), and its focus is (-1,2). what is the standard form of the parabola?

The standard form of the equation of the parabola with vertex (-5, 2) and focus (-1, 2) is

The vertex of the parabola (h, k) = (-5, 2)

That is, h = -5, k = 2

The focus (4p, k) = (-1, 2)

From the relationship above:

4p  = -1

p = -1/4

The equation of a parabola is given as:

Substitute h = -5, k = 2, p = -1/4 into the parabola equation above

Simplifying the equation above

Simplifying further, we have:

Therefore, the equation of the parabola with vertex (-5, 2) and focus (-1, 2) is

Learn more here on standard form of a parabola here: link

Check the picture below.  So the parabola looks more or less like so.