Question 1178990
.
A circle and straight line intersect in the points (−2, 6) and (6, −2). Determine 
the equation of the circle and the line.
~~~~~~~~~~~~~~~



There is only one straight line,  passing through two given points on the plane,


so it is  POSSIBLE  to determine its equation.



In opposite,  there are  INFINITELY  MANY  circles on the plane passing through the two given points.



Therefore,  your problem,  as it is worded,  printed,  posted and presented,


<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;M A K E S &nbsp;&nbsp;no &nbsp;&nbsp;S E N S E.</H3>


Unfortunately   &nbsp;&nbsp;&nbsp;&nbsp;(or fortunately . . . )



I don't know what is the source of this problem, who composed it and for what reason . . . 



But the fact and the diagnosis is as it is stated above.



Do not forget to submit your "THANKS" to me for pointing the defects in your post/problem.