Given that we need to find the length of the chord of the parabola y2 = 4ax which passes through the vertex and is inclines to axis at .
We know that the vertex and axis of the parabola y2 = 4ax is (0, 0) and y = 0(x - axis).
We know that the equation of the straight line passing through the origin and inclines to the x - axis at an angle θ is y = tanθx.
⇒ y = 1.x
⇒ y = x.
The equation of the chord is y = x.
Substituting y = x in the equation of parabola.
⇒ x2 = 4ax
⇒ x = 4a.
⇒ y = x = 4a
The chord passes through the points (0, 0) and (4a, 4a).
We know that the distance between the two points (x1, y1) and (x2, y2) is .
⇒ l = 4√2 a
∴The correct option is A
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