Circle equation homework

The equation of a circle is ( x 2 5) 2 1 (y 2 1) 2 5 9. Without sketching the circle, tell whether the point is on the circle, inside the circle, or outside the circle. a. Substitute the coordinates of the point into the equation.

The answer is to Complete the Square (read about that) twice ... once for x and once for y: Now complete the square for x (take half of the −2, square it, and add to both sides): And complete the square for y (take half of the −4, square it, and add to both sides):

A circle is easy to make: from a central point. from the center. Circle: The set of all points on a plane that are a fixed distance from a center. Now let's work out exactly where all the points are. And then use Pythagoras: y ≈ ±4.58... And here are the two points:

So the circle is all the points (x,y) that are "r" away from the center (a,b). Now lets work out where the points are (using a right-angled triangle and Pythagoras ): It is the same idea as before, but we need to subtract a and b: