Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points)

y^2 = -12x

y^2 = -3x

y = negative x^2 divided by 12

y = negative x^2 divided by 3

From given option ,  the equation of parabola is                                            y = negative x² divided by 12

Step-by-step explanation:

Given as for parabola :

The focus is at (0 , - 3)

The directrix equation is y = 3

Now, equation of parabola parallel to y-axis is

( x - h )² = 4 p ( y - k )

where focus is ( h , k+p )   and  directrix equation is y = k - p

So, from equation

h  = 0     and   k + p = - 3

And y = k - p   i.e k - p = 3

Now solving  ( k + p ) + (  k - p ) = - 3 + 3

or, 2 k = 0  ∴ k = 0

Put the value of k , k + p = - 3

So, 0 + p = - 3    ∴ p = - 3

Now equation of parabola with h = 0  , k = 0  , p = - 3

( x - h )² = 4 p ( y - k )

I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )

Or, x² = - 12 y   is the equation of parabola

Hence  From given option ,  the equation of parabola is                                y = negative x² divided by 12       Answer

the answer is c.

for continuous functions, they continue in the same pattern and you have to find that pattern kinda like slope

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12