What is the equation of a parabola with (-1, - 3) as its focus and y = 1 as its directrix? Enter the equation in the box.

The answer

the general formula showing parabola is

y = ax² + bx + c, its standard form is y = a (x-h) ² + k

the focus formula is

F (h, k + 1 / 4a) and the directrix is

the directrix is V (k - 1/4a)

so he equation of a parabola with (-1, - 3) as its focus implies

(h, k + 1 / 4a) = (-1, - 3)

h = - 1, and k + 1 / 4a = - 3

the directrix is k - 1/4a = 1

we should solve the system of equation

k + 1 / 4a = - 3

k - 1/4a = 1

2k = - 3+1 = - 2, so k = - 1 and when we use this value

-1 - 1/4a = 1 implies 2 = - 1/4a this equation give a = - 1/8

finally the equation is

y = - 1/8 (x + 1) ² - 1