Question

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

Answer 1

Answer:

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