Question 1012679
you have two equations that need to be solved simultaneously.


the solution will be common to both equations.


the equations are:


x^2 + y^2 - 6x - 8y + 9 = 0


y = x


replace y with x in the first equataion to get x^2 + x^2 - 6x - 8x + 9 = 0


combine like terms to get 2x^2 - 14x + 9 = 0


solve this quadratic equation to get x = .71612 or x = 6.28388 rounded to 5 decimal places.


since y = x, the coordinate points are (.71612,.71612) or (6.28388,6.28388).


these points are the points of intersection between the circle and the secant line.


the formula for the length of that secant line is L = sqrt((x2-x1)^2 + (y2-y1)^2).


that becomes L = sqrt((6.28388-.71612)^2 + (6.28388-.71612)^2).


this results in L = 7.874 rounded to 3 decimal places.


you can also find the intersection points by graphing as shown below.


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