Consider the parabola with a focus at the point (0,-3) and directrix y=2 . which two equations can be used to correctly relate the distance from the focus and the directrix to any point (x, y) on the parabola ?

The equation of parabola is x² + 20 y + 60 = 0

Step-by-step explanation:

Given as :

The focus point of parabola = (0 , - 3)

The directrix is y = 2

The equation of parabola  in vertex form is written as

(x - h)² = 4 p (y -k)

where (h , k) = (0, - 3)

And directrix y = k - p

So , 2 = k - p

Or p = k - 2

Or, p = - 3 - 2

∴   p = - 5

So, the equation of parabola is

(x - 0)² = 4 × ( - 5 ) (y + 3)

or, x² = - 20 ( y + 3)

or, x² = - 20 y - 60

Hence The equation of parabola is x² + 20 y + 60 = 0   Answer

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