Circle Equation Mastery

The equation of a circle with diameter joining points A and B can be found using the midpoint formula and the distance formula. The center of the circle is the midpoint of the line segment AB, and the radius is half the length of AB.

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by $((x1 + x2)/2, (y1 + y2)/2)$.

The distance formula calculates the distance between two points (x1, y1) and (x2, y2) as $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$.

<p>The center of the circle is the midpoint of the line segment AB, which can be found using the midpoint formula: $((2-1)/2, (-3+4)/2)$, giving us the center (0.5, 0.5). The radius of the circle is half the length of AB, which can be found using the distance formula: $\sqrt{((-1-2)^2 + (4-(-3))^2)}/2$, giving us the radius $\sqrt{50}/2$. Therefore, the equation of the circle is $(x-0.5)^2 + (y-0.5)^2 = 25$.</p> Signup and view all the answers

<p>The center of the circle is the midpoint of the line segment AB, which can be found using the midpoint formula: $((2-1)/2, (-3+4)/2)$, giving us the center (0.5, 0.5).</p> Signup and view all the answers

<p>The radius of the circle is half the length of AB, which can be found using the distance formula: $\sqrt{((-1-2)^2 + (4-(-3))^2)}/2$, giving us the radius $\sqrt{50}/2$.</p> Signup and view all the answers