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General equation of parabola that is symmetric with respect to x-axis direction is

....................... (1)

Directrix of parabola given by above equation is

  ........................(2)

Given parabola is  

Above equation of parabola is written as

.......................... (3)

By comparing eqn.(1) and eqn.(3) , we get  α = 8/k ,  a = 1/k

Hence by substituting α and a , eqn.(2) is written as

.............................. (4)

Given directrix equation is , x = 1 .................(5)

By equating (4) and (5) , we get

from above expression , we get the following quadratic equation

k² + 4 k - 32 = 0

By solving above quadratic expressiojn, we get k = -8 or k =4