Find the equation of the parabola with directrix y 32 and f

Find the equation of the parabola with directrix: y = 3/2 and focus: (0, -3/2) Find the Focus, Vertex, and the equation of the Directrix of the parabola given by the equation: y^2 = --I2x

Solution

1) y = 3/2 , focus = ( 0 , -3/2)

equation of parabola is

-6y = x^2

2) y^2 = -12 x

p = -12/ 4 = - 3

Focus : (h + p , k)

h = 0 , k = 0

Focus = (-3, 0)

Vertex = (0, 0 )

Diretrix : x = k - p = 0 - ( -3) = 3

x = 3