determine the equation of a circle that has its center a (0,0) and passes through each point.

a)(6,-3)

well, since the equation will be

x^2+y^2 = r^2

just plug in your values for x and y, and that will give you the necessary r.

To determine the equation of a circle with its center at (0,0) and passing through a given point, we need to find the radius of the circle first.

The distance between the center of the circle (0,0) and the point (6,-3) is the radius of the circle. We can use the distance formula to calculate this distance:

Radius = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values, we get:

Radius = √((6 - 0)^2 + (-3 - 0)^2)
= √(6^2 + (-3)^2)
= √(36 + 9)
= √45

So the radius of the circle is √45.

Now that we have the center (0,0) and the radius √45, we can write the equation of the circle in the standard form:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the center of the circle and r represents the radius.

Plugging in the values, the equation of the circle is:

(x - 0)^2 + (y - 0)^2 = (√45)^2
x^2 + y^2 = 45

Therefore, the equation of the circle is x^2 + y^2 = 45