Explanation:

To find the point where all the chords of the parabola y^2 = 4x subtend a right angle at the origin, we need to consider the equation of a chord.

Equation of a Chord:
The equation of a chord of a parabola y^2 = 4ax is given by:
y = mx + a/m

where m is the slope of the chord.

Subtending a Right Angle at the Origin:
For a chord to subtend a right angle at the origin, the product of the slopes of the perpendicular chords should be -1.

So, let's find the slopes of two perpendicular chords using their equations.

First Chord:
For the first chord, let's consider a point (x1, y1) on the parabola. The slope of the first chord passing through this point is given by:
m1 = (y1 - 0) / (x1 - a/m1)
m1 = y1 / (x1 - a/m1)

Second Chord:
For the second chord, let's consider a point (x2, y2) on the parabola. The slope of the second chord passing through this point is given by:
m2 = (y2 - 0) / (x2 - a/m2)
m2 = y2 / (x2 - a/m2)

Now, we can find the product of the slopes of these two perpendicular chords:
m1 * m2 = (y1 / (x1 - a/m1)) * (y2 / (x2 - a/m2))
m1 * m2 = (y1 * y2) / ((x1 - a/m1) * (x2 - a/m2))

Substituting the Equation of the Parabola:
Since the given parabola is y^2 = 4x, we can substitute y^2 = 4x in the above equation:
m1 * m2 = (4x1 * 4x2) / ((x1 - a/m1) * (x2 - a/m2))
m1 * m2 = 16x1x2 / ((x1 - a/m1) * (x2 - a/m2))

Concurrent Point:
For all chords to be concurrent, the product of the slopes should be the same for any two randomly selected points on the parabola.

Let's consider two points on the parabola, (x1, y1) and (x2, y2), and find the product of their slopes:
m1 * m2 = 16x1x2 / ((x1 - a/m1) * (x2 - a/m2))

Since this product is independent of the points chosen, let's consider the origin (0, 0) and another point (x, y) on the parabola.

Substituting the Values:
m1 * m2 = 16(0)(x) / ((0 - a/m1) * (x - a/m2))
m1 * m2 = 0 / (-ax - a/m2)

Simplifying the equation, we get:
m1 * m2 = 0