Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.

y2 = -12x

y2 = -3x

y = negative 1 divided by 12 x2

y = negative 1 divided by 3 x2

Option 3 : y = negative 1 divided by 12 x^2

The standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3 is

Solution:

Given that, parabola has a focus at (0, -3) and directrix at y = 3.

We have to find the parabola equation in standard form.

The standard form of parabola is given as:

Where the focus is (h, k + p) and the directrix is y = k - p

So, here, (h, k + p) = (0, -3)  

And y = k – p  

y = 3

By comparison, h = 0, k + p = - 3 ------  eqn (2)  

k – p = 3 ------ eqn (3)

Add (2) and (3)

k + p = -3

k – p = 3

(+)---------------

2k = 0

k = 0

Then, from (2) 0 + p = - 3

So, h = 0, k = 0, and p = -3

Now, put these values in (1)

So option 3 is correct

a² + b²= c²

24² + 7² = c²

c= 25

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.