Question 1158991
Find an equation for the line that goes through the two intersection points of the circle
x2 +y2 =25andthecircle(x−8)2 +(y−4)2 =65.
<pre>The points where the circles intersect each other are the solutions to the 2 equations. 
The 2 points of intersection are connected by a line, and that line is the equation that's being sought!
Therefore, we get: {{{system(matrix(1,6, x^2 + y^2, ""="", 25, "----------------", eq, "(i)"), and, matrix(1,3, (x - 8)^2 + (y - 4)^2, ""="", 65),
matrix(1,3, x^2 - 16x + 64 + y^2 - 8y + 16, ""="", 65),
matrix(1,6, x^2 + y^2 - 16x  - 8y + 80, ""="", 65, "----", eq, "(ii)"))}}}
       Therefore, we get: 25 - 16x - 8y + 80 = 65 ------ Substituting 25 for x<sup>2</sup> + y<sup>2</sup> in eq (ii)
                             - 16x - 8y = - 40_____- 8(2x + y) = - 8(5) =====> {{{highlight_green(matrix(1,4, "Equation:", 2x + y, "=", 5))}}}