Question

Which of these is the best definition of a circle? A. The set of all points in a plane that are equidistant from a single point and a line B. The set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant C. The set of all points in a plane that are a certain distance from a single point D. The set of all points in a plane for which the difference between the distances to two fixed points equals a certain constant

Answer 1

The right answer is C. The set of all points in a plane that are a certain distance from a single point

The certain distance is called the radius and the single point is called the center. In this way, all points are a certain or, in other words, the same distance from the center. So, for the Standard Form of the Equation of a Circle we have that:

$The \ point \ (x,y) \ lies \ on \ the \ circle \ of \\ \mathbf{radius} \ r \ and \ \mathbf{center} \ (h,k) \ if \ and \ only \ if :\\ \\ (x-h)^2+(y-k)^2=r^2$

Answer 2

The answer is C for APEX