Çözüldü Integration - Derivative - Coordinate Geometry

A classic exam (calculator usage is permitted) adaptation of a solved problem from Texas Tech University for science high school:

For a curve such that the slope at any point is equal to the square of the product of its coordinates, and the distance from the origin of the Cartesian plane to the point where it intersects the y-axis in the positive direction is 2 units, what is the distance from the origin to the line segment connecting the point of tangency, where the abscissa is 1 / 2, to the point at which the tangent line intersects the x-axis?


https://i.ibb.co/GGw4XbP/Texas-Tech.png
https://wetalldid.wordpress.com/wp-...-for-engineers-and-scientists-1-alex-wang.pdf
(First question)

y = f(x) = 6 / (3 - 2x^3) ⇒ f(1 / 2) = 6 / [ 3 - 2(1 / 2^3) ] = 24 / 11
Slope of the tangent line: m = [ (1 / 2)(24 / 11) ]^2 = (12 / 11)^2
Equation of the tangent line: y - 24 / 11 = [ (12 / 11)^2 ]·(x - 1 / 2)
Abscissa of the point at which the tangent line intersects the x-axis: 0 - 24 / 11 = [ (12 / 11)^2 ]·(x - 1 / 2) ⇒ x = -4 / 3
Line passing (-4 / 3, 0) and (1 / 2, 24 / 11): (y - 0) / (0 - 24 / 11) = [ x - (-4 / 3) ] / (-4 / 3 - 1 / 2) ⇒ 144x - 121y + 192 = 0
Distance from the origin to the tangent line: |144·0 + (-121)·0 + 192| / (12^4 + 11^4)^0.5 = 192 / √35377 units (≈ 1.021)

Check by WolframAlpha:

https://i.ibb.co/RGwqD70n/Texas-Tech-WA.png
https://www.wolframalpha.com/input?...-4 / 3, 0) and (1 / 2, 24 / 11) to the origin

Graph:

https://i.ibb.co/wNp2gsDb/Texas-Tech.png

Turkish Translation of The Question:
Herhangi bir noktasındaki eğimi o noktadaki koordinatlarının çarpımının karesine eşit olan ve ordinatlar eksenini pozitif yönde kestiği noktanın da orijine uzaklığı 2 birim olan eğrinin apsisi 1 / 2 olan noktasındaki teğetinin x eksenini kestiği noktayla teğetin değme noktasını birleştiren doğruya orijinin uzaklığı kaç birimdir?