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

Answer:

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

$Where\ p$

Step-by-step 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

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

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

$Where p$