Explanation:
there are many possibilities, 4 of them really easy.
the endpoint of a diameter is simply a point on the circle arc.
the easy options are to assume that the center of the circle is on the x- or the y-axis.
let's go with the x-axis (we only need 2 circles : one with the center left, and one with the center right of the origin).
we know the radius is 3.
so, the center of either circle is 3 units away from the origin.
so, center of circle1 = (-3, 0), center of circle2 = (3, 0).
the equation for a circle is
(x - h)² + (y - k)² = r²
r is the radius, (h, k) is the center point.
equation for circle1 :
(x - -3)² + (y - 0)² = 3²
(x + 3)² + y² = 9
equation for circle2 :
(x - 3)² + (y - 0)² = 3²
(x - 3)² + y² = 9
you see ?
the other 2 easy options would be to put the centers on the y-axis : (0, -3) and (0, 3)