Max and min line equation

[leprofece]

1) If P (a, b) is a fixed point located in the first quadrant. Find the equation of the straight line which, passing through P, is such that the length of the segment that on it limits the semiaxes positives is minimal. Calculate the segment lenght

Answers
y-b = Cubic sqrt ((b)/a) (x-a)

L^2/3 = a^2/3 + b ^2/3

Equation y-b = m(x-a)
According to the answer I must get the slope m derivating what?

 

[Evgeny.Makarov]

Determine the $x$ and $y$ intercepts of the line, then find the square of the line segment as a function of $m$ using the Pythagorean theorem. Differentiating it produces an expression containing $m$, $1/m^2$ and $1/m^3$, i.e., essentially a quartic equation. It may be tricky to solve it, but it is easy to verify that $m=-\sqrt[3]{\dfrac{b}{a}}$ is root.