Tough question.

The first part of the solution:Let the origin be O.

The area of the triangle ABC is 1/8.

The area of the triangle ABC = the area of the triangle AOB*2

The area of the triangle AOB = (distance between Origin and B * distance between Origin and A)/2

The area of the triangle ABC = ((distance between Origin and B * distance between Origin and A)/2)*2 =>

The area of the triangle ABC = distance between Origin and B * distance between Origin and A = 1/8

The second part of the solution:Point A is the point when x=0

If x=0, then y=k-0 => y=k

So, we now know that the distance between the origin and the point A is

k.

Points B and C are points when y=0

0=k-x^2 => x^2 = k => x = +- sqrt(k)

So, we now know that the distance between the origin and the point B is

sqrt(k)The third part of the solution:k*sqrt(k) = 1/8

k^3 = 1/64

k = 1/sqrt(8)

k = 0.35

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