Find the coordinates of a point equidistant from (1,-6), (5,-6), and (6,-1).
Please help me and show the solution... thanks!
There may be several approaches. One is to find the slope between two of the points, and then the mid-point of those two. That, the negative reciprocal of the slope, and a point, will give you the equation of the line that is the perpendicular bisector of those two points. Use another two points and do the same. You now have two lines that will pass through the center of the circumcircle of the triangle formed by the three points. Solve that system for the point of intersection, the center of that circle.
Give it a try, and try showing some initial personal effort on some of the others you have posted if you want help there as well. If this is an assignment, even a hint is really not fair to other students who are perhaps more diligent or more capable, and your results would not reflect your true capability. Some of these questions require some insight, and that done the rest is relatively very simple. In fact, the real question is to determine whether or not you have the necessary insight to solve problems such as this, which are non-standard textbook problems. So, for us to do it, even to give a hint, spoils the initial intent of the questions altogether.