You don't even have to consider which quadrants the line is in, just start solving for that line and the lines y=x and y=-x.The formula for finding the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center point of the circle and r is the radius.
To find the center and radius of a circle given three points on the circle, you can use the formula (x1 + x2 + x3)/3 = h and (y1 + y2 + y3)/3 = k to find the center point (h,k). Then, you can use the distance formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2) to find the radius.
No, the Pythagorean theorem is used to find the length of the sides of a right triangle, not the equation of a circle.
At least three points are needed to determine the equation of a circle. However, more points can be used to ensure accuracy and to check for consistency.
The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center point and r is the radius. The general form, on the other hand, is x^2 + y^2 + Dx + Ey + F = 0, where D, E, and F are constants. The standard form is easier to use for graphing and finding the center and radius, while the general form is useful for finding the equation of a circle when given other information such as the diameter or points on the circle.