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
