Given the equation of the parabola - 36y = ?

The focus of the parabola is:

(0,9)

(-9,0)

(0,-9)

Correct question is;

Given the equation of the parabola x² = - 36y

The focus of the parabola is:

Answer:

Option C - Focus = (0,-9)

Step-by-step explanation:

The equation of the parabola is:

x² = - 36y

Thus, y = - x²/36

Using the vertex form,

y = a (x - h) ² + k, to determine the values of a, h, and k.

We will have;

y = (-1/36) (x - 0) ² + 0

Thus,

a = - 1/36

h = 0

k = 0

The distance (p) from the vertex to a focus of the parabola is gotten by using the following formula.

p = 1/4a

So, p = 1 / (4 * (-1/36))

p = - 1 / (1/9)

p = - 9

Now, The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

Focus is (h, k+p)

Plugging in the relevant values, we have;

Focus = (0, (0 + (-9))

Focus = (0,-9)