Question

The focus of a parabola is (-4, -5), and its directrix is y = -1. What is the formula for the parabola in standard form.

Answer 1

`(x - (-4))^2 = -8(y - (-3))`

`Where\ p<0`

Explanation:

From the question we are told that:

Parabola focus co-ordinates

`F=(-4, -5)\\Directrix is y = -1`

Generally the equation for standard form of Parabola is mathematically given by

`(x - h)^2 = 4p(y - k)`

where p≠ 0

Generally the equation for Directrix of Parabola is mathematically given by

`y=k-p\\y=-1`

Generally the equation for Focus of Parabola F is mathematically given by

`F=(h, k + p).`

`F=(-4, -5)`

Therefore

`k-p=-1`

`k=-1+p`

Given

`k+p=-5`

`-1+p+p=-5`

`2p=-4`

`p=-2`

Therefore

`k-p=-1`

`k-(-2)=-1`

`k=-3`

Generally the equation for standard form of Parabola is mathematically given by

`(x - (-4))^2 = 4(-2)(y - (-3))`

`(x - (-4))^2 = -8(y - (-3))`

`Where p<0`