Question

Find the properties of the parabola with the equation (x + 5) 2 = 4(y - 1)

Focus

a. (-5, 2)
b. (-5, 0)
c. (-5, 5)

Answer 1

Option a. (-5, 2)

Explanation:

The focus of a parabola is a point. Regarding this point, each point of the parabola has the same distance to a line that is known as "directrix".

By definition, for a parabola of the form:

`(x-h)^2 = 4p(y-k)`

The focus of the parable is given by the point: (h, k +p)

We must identify the values of h, k and p for the given equation.

`(x + 5)^2 = 4(y - 1)`

`h = -5\\k = 1\\4p = 4\\p =1`

Now that we know the values of h, k and p we can find the focus

The focus is

(-5, 1+1)

(-5, 2).