SOLUTION: I am not even sure what topic this problem falls under. It says, "Find the standard form of the equation of the circle for which the endpoints of a diameter are (0,0)and (4, -6).

Algebra ->  Systems-of-equations -> SOLUTION: I am not even sure what topic this problem falls under. It says, "Find the standard form of the equation of the circle for which the endpoints of a diameter are (0,0)and (4, -6).       Log On


   

Question 705215: I am not even sure what topic this problem falls under. It says, "Find the standard form of the equation of the circle for which the endpoints of a diameter are (0,0)and (4, -6).
Can you please help me with this?
Thanks!
Melissa
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If (0,0) and (4,-6) are endpoints of a diameter,
the midpoint of that diameter is the center of the circle.
Its coordinates are found by averaging the coordinates of those endpoints.
The x-coordinate is %280%2B4%29%2F2=highlight%282%29.
The y-coordinate is %280%2B%28-6%29%29%2F2=highlight%28-3%29
So, we have the center, C(2,-3).

A picture is work a thousand words:
The radius, R, is the length of the segment form (0,0) to C(2,-3).
That segment is the hypotenuse of a right triangle (drawn in green).
We can calculate R%5E2 based on the Pythagorean theorem
R%5E2=2%5E2%2B3%5E2 --> R%5E2=4%2B9 --> R%5E2=highlight%2813%29
Any point (x,y) in the circle is at the same distance R from the center, C.
As a consequence
%28x-2%29%5E2%2B%28y-%28-3%29%29%5E2=R%5E2 --> highlight%28%28x-2%29%5E2%2B%28y%2B3%29%5E2=13%29