Dear student,

Thedirectrixis perpendicular line to the axis of symmetry of a parabola and does not touch the parabola. It is equal to the distance that focus make from the origin but in opposite direction.

For a parabola having the equation as y^2 = 4ax
The equation of directrix is x = -a

Now the equation of the parabola is given as y^2 = 10x
So comparing it with standard form, we get 4a=10
Therefore a = 5/2

So, the equation of directrix for y^2 = 10x is

x = - 5/2