find the equatn of a circle with (a).centre (1,2) and radius 3.(b) centre (1,-3) and radius 2
To find the equation of a circle, we use the formula:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the coordinates of the center of the circle, and r represents the radius.
(a) The center of the circle is given as (1, 2) and the radius is 3.
Using the formula, we substitute the values into the equation:
(x - 1)^2 + (y - 2)^2 = 3^2
Simplifying:
(x - 1)^2 + (y - 2)^2 = 9
Therefore, the equation of the circle with center (1, 2) and radius 3 is (x - 1)^2 + (y - 2)^2 = 9.
(b) The center of the circle is given as (1, -3) and the radius is 2.
Using the formula, we substitute the values into the equation:
(x - 1)^2 + (y - (-3))^2 = 2^2
Simplifying:
(x - 1)^2 + (y + 3)^2 = 4
Therefore, the equation of the circle with center (1, -3) and radius 2 is (x - 1)^2 + (y + 3)^2 = 4.