Question

Suppose a parabola with focus at $(0,0)$ has $x - y + 1 = 0$ as its tangent at the vertex. Then the equation of its directrix is

• A. $x - y + 2 = 0$
• B. $x - y - 2 = 0$
• C. $x - y + 3 = 0$
• D. $x - y + 4 = 0$

Hint:

Directrix is symmetric about vertex and lies along the axis of the parabola.

Answer 1

The Correct Option is A

Focus = $(0,0)$ and vertex lies on the line $x - y + 1 = 0$
The axis of the parabola is perpendicular to the tangent, hence along line $x - y + 1 = 0$
Vertex lies midway between focus and directrix
So, find line parallel to tangent that is at same distance on the other side of focus
That line is $x - y + 2 = 0$