Question

Prove that the area of the triangle around which the tangent is to the coupling curve, y = 1/x , at this point (a, 1/a) where a > zero , And around the two coordinate axes, , equal 2 (Square unit) With chart.​

Answer 1

Hi,

Explanation:

Let's assume (a,1/a) the tangent point.

Slope of the tangent: y'(a)=-1/a²

Equation of the tangent: y-1/a=-1/a² * (x -a) or y=-1/a² *x +2/a

x-intercept: y=0 => -1/a²*x+2/a=0 => x=2/a * a² =2a

y-intercept: x=0 => y=2/a

Area of the triangle AEF=2a*2/a /2 =2