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

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

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