The first question. Let point b (m, n) be in the first quadrant, then tan∠POB=n/m= 1/9, and m=9n, and point b is on the image of function y= 1/x, and n= 1/m, so m =

And AB//x axis, so point A( 1/3, 1/3), so AB=3- 1/3=8/3.

The second question. . . Conditionally, it is known that the parabolic opening is downward. Let a (1). A), B( 1/a, a), then AB= 1/a-a=8/3.

So 3a? +8a-3=0。 A equals -3 or 1/3.

When a=-3, point A(-3. -3) and B(- 1/3, -3) are (-5/3). -5/3) Because the vertex is on y=x, we can set the quadratic function y=k(x+5/3). -5/3, point A is replaced. The solution is k=-3/4.

So the resolution function is y=-3/4(x+5/3)? -5/3

In the same way. When a= 1/3 is yes, then the resolution function is y=-3/4(x-5/3)? +5/3.

The third question. Let A(a, a) b (1/a. a). According to the conditions, the symmetry axis of parabola is x=a/2+ 1/2a.

Let the quadratic resolution function be y=9/5(x-2)(x-(a+ 1/a)+2).

Point A(a, a) is replaced. If the solution is a 1=3 and a2=6/ 13, then the distance from point P to straight line AB is 3 or 6/ 13.

For example, 1/2 is half. . Can't score