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

Mathematics

1 answer:

Tanya [424]3 years ago

8 0

Answer:

Option a. (-5, 2)

Step-by-step 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).

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