Question

Review the graph of circle A. On a coordinate plane, a circle has center A (1, 1) and point B (5, 4) is on the edge of the circle. A line goes from point A to point B. Which equation represents circle A? (x – 1)2 + (y – 1)2 = 5 (x + 1)2 + (y + 1)2 = 5 (x – 1)2 + (y – 1)2 = 25 (x + 1)2 + (y + 1)2 = 25

Answer 1

(x - 1)² + (y - 1)² = 25

Explanation:

the distance from the center of the circle to any point on the edge (or arc) of the circle is the radius of the circle.

per the distance formula (= Pythagoras for the right-angled triangle of the coordinate differences between the 2 points) we know

AB² = (xb - xa)² + (yb - ya)² = (5 - 1)² + (4 - 1)² =

= 4² + 3² = 16 + 9 = 25

AB = radius = 5

the standard form of a circle is

(x - h)² + (y - k)² = r²

(h, k) being the coordinates of the center of the circle, r being the radius.

(x - 1)² + (y - 1)² = 25

is the correct equation.